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Simplifying (2.22x2) + (5.65x) + -1(1.95) = (3.31x) + (5.71x2) + -1(7.27) Multiply -1 * 1.95 (2.22x2) + (5.65x) + -1.95 = (3.31x) + (5.71x2) + -1(7.27) Reorder the terms: -1.95 + (5.65x) + (2.22x2) = (3.31x) + (5.71x2) + -1(7.27) Multiply -1 * 7.27 -1.95 + (5.65x) + (2.22x2) = (3.31x) + (5.71x2) + -7.27 Reorder the terms: -1.95 + (5.65x) + (2.22x2) = -7.27 + (3.31x) + (5.71x2) Solving -1.95 + (5.65x) + (2.22x2) = -7.27 + (3.31x) + (5.71x2) Solving for variable 'x'. Reorder the terms: -1.95 + 7.27 + (5.65x) + (-3.31x) + (2.22x2) + (-5.71x2) = -7.27 + (3.31x) + (5.71x2) + 7.27 + (-3.31x) + (-5.71x2) Combine like terms: -1.95 + 7.27 = 5.32 5.32 + (5.65x) + (-3.31x) + (2.22x2) + (-5.71x2) = -7.27 + (3.31x) + (5.71x2) + 7.27 + (-3.31x) + (-5.71x2) Combine like terms: (5.65x) + (-3.31x) = 2.34x 5.32 + 2.34x + (2.22x2) + (-5.71x2) = -7.27 + (3.31x) + (5.71x2) + 7.27 + (-3.31x) + (-5.71x2) Combine like terms: (2.22x2) + (-5.71x2) = -3.49x2 5.32 + 2.34x + -3.49x2 = -7.27 + (3.31x) + (5.71x2) + 7.27 + (-3.31x) + (-5.71x2) Reorder the terms: 5.32 + 2.34x + -3.49x2 = -7.27 + 7.27 + (3.31x) + (-3.31x) + (5.71x2) + (-5.71x2) Combine like terms: -7.27 + 7.27 = 0.00 5.32 + 2.34x + -3.49x2 = 0.00 + (3.31x) + (-3.31x) + (5.71x2) + (-5.71x2) 5.32 + 2.34x + -3.49x2 = (3.31x) + (-3.31x) + (5.71x2) + (-5.71x2) Combine like terms: (3.31x) + (-3.31x) = 0.00 5.32 + 2.34x + -3.49x2 = 0.00 + (5.71x2) + (-5.71x2) 5.32 + 2.34x + -3.49x2 = (5.71x2) + (-5.71x2) Combine like terms: (5.71x2) + (-5.71x2) = 0.00 5.32 + 2.34x + -3.49x2 = 0.00 Begin completing the square. Divide all terms by -3.49 the coefficient of the squared term: Divide each side by '-3.49'. -1.524355301 + -0.670487106x + x2 = 0 Move the constant term to the right: Add '1.524355301' to each side of the equation. -1.524355301 + -0.670487106x + 1.524355301 + x2 = 0 + 1.524355301 Reorder the terms: -1.524355301 + 1.524355301 + -0.670487106x + x2 = 0 + 1.524355301 Combine like terms: -1.524355301 + 1.524355301 = 0.000000000 0.000000000 + -0.670487106x + x2 = 0 + 1.524355301 -0.670487106x + x2 = 0 + 1.524355301 Combine like terms: 0 + 1.524355301 = 1.524355301 -0.670487106x + x2 = 1.524355301 The x term is -0.670487106x. Take half its coefficient (-0.335243553). Square it (0.1123882398) and add it to both sides. Add '0.1123882398' to each side of the equation. -0.670487106x + 0.1123882398 + x2 = 1.524355301 + 0.1123882398 Reorder the terms: 0.1123882398 + -0.670487106x + x2 = 1.524355301 + 0.1123882398 Combine like terms: 1.524355301 + 0.1123882398 = 1.6367435408 0.1123882398 + -0.670487106x + x2 = 1.6367435408 Factor a perfect square on the left side: (x + -0.335243553)(x + -0.335243553) = 1.6367435408 Calculate the square root of the right side: 1.279352782 Break this problem into two subproblems by setting (x + -0.335243553) equal to 1.279352782 and -1.279352782.Subproblem 1
x + -0.335243553 = 1.279352782 Simplifying x + -0.335243553 = 1.279352782 Reorder the terms: -0.335243553 + x = 1.279352782 Solving -0.335243553 + x = 1.279352782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.335243553' to each side of the equation. -0.335243553 + 0.335243553 + x = 1.279352782 + 0.335243553 Combine like terms: -0.335243553 + 0.335243553 = 0.000000000 0.000000000 + x = 1.279352782 + 0.335243553 x = 1.279352782 + 0.335243553 Combine like terms: 1.279352782 + 0.335243553 = 1.614596335 x = 1.614596335 Simplifying x = 1.614596335Subproblem 2
x + -0.335243553 = -1.279352782 Simplifying x + -0.335243553 = -1.279352782 Reorder the terms: -0.335243553 + x = -1.279352782 Solving -0.335243553 + x = -1.279352782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.335243553' to each side of the equation. -0.335243553 + 0.335243553 + x = -1.279352782 + 0.335243553 Combine like terms: -0.335243553 + 0.335243553 = 0.000000000 0.000000000 + x = -1.279352782 + 0.335243553 x = -1.279352782 + 0.335243553 Combine like terms: -1.279352782 + 0.335243553 = -0.944109229 x = -0.944109229 Simplifying x = -0.944109229Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.614596335, -0.944109229}
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