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Simplifying 2x2 + 3x + -7 = 9 Reorder the terms: -7 + 3x + 2x2 = 9 Solving -7 + 3x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -7 + -9 + 3x + 2x2 = 9 + -9 Combine like terms: -7 + -9 = -16 -16 + 3x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -16 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + 1.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 1.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 1.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 1.5x + x2 = 0 + 8 1.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 1.5x + x2 = 8 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 8 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 8 + 0.5625 Combine like terms: 8 + 0.5625 = 8.5625 0.5625 + 1.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + 0.75) equal to 2.926174978 and -2.926174978.Subproblem 1
x + 0.75 = 2.926174978 Simplifying x + 0.75 = 2.926174978 Reorder the terms: 0.75 + x = 2.926174978 Solving 0.75 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.926174978 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.926174978 + -0.75 x = 2.926174978 + -0.75 Combine like terms: 2.926174978 + -0.75 = 2.176174978 x = 2.176174978 Simplifying x = 2.176174978Subproblem 2
x + 0.75 = -2.926174978 Simplifying x + 0.75 = -2.926174978 Reorder the terms: 0.75 + x = -2.926174978 Solving 0.75 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.926174978 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.926174978 + -0.75 x = -2.926174978 + -0.75 Combine like terms: -2.926174978 + -0.75 = -3.676174978 x = -3.676174978 Simplifying x = -3.676174978Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.176174978, -3.676174978}
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