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Simplifying -16x2 + 140x + 50 = x Reorder the terms: 50 + 140x + -16x2 = x Solving 50 + 140x + -16x2 = x Solving for variable 'x'. Reorder the terms: 50 + 140x + -1x + -16x2 = x + -1x Combine like terms: 140x + -1x = 139x 50 + 139x + -16x2 = x + -1x Combine like terms: x + -1x = 0 50 + 139x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -3.125 + -8.6875x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -8.6875x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -8.6875x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -8.6875x + x2 = 0 + 3.125 -8.6875x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -8.6875x + x2 = 3.125 The x term is -8.6875x. Take half its coefficient (-4.34375). Square it (18.86816406) and add it to both sides. Add '18.86816406' to each side of the equation. -8.6875x + 18.86816406 + x2 = 3.125 + 18.86816406 Reorder the terms: 18.86816406 + -8.6875x + x2 = 3.125 + 18.86816406 Combine like terms: 3.125 + 18.86816406 = 21.99316406 18.86816406 + -8.6875x + x2 = 21.99316406 Factor a perfect square on the left side: (x + -4.34375)(x + -4.34375) = 21.99316406 Calculate the square root of the right side: 4.68968699 Break this problem into two subproblems by setting (x + -4.34375) equal to 4.68968699 and -4.68968699.Subproblem 1
x + -4.34375 = 4.68968699 Simplifying x + -4.34375 = 4.68968699 Reorder the terms: -4.34375 + x = 4.68968699 Solving -4.34375 + x = 4.68968699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.34375' to each side of the equation. -4.34375 + 4.34375 + x = 4.68968699 + 4.34375 Combine like terms: -4.34375 + 4.34375 = 0.00000 0.00000 + x = 4.68968699 + 4.34375 x = 4.68968699 + 4.34375 Combine like terms: 4.68968699 + 4.34375 = 9.03343699 x = 9.03343699 Simplifying x = 9.03343699Subproblem 2
x + -4.34375 = -4.68968699 Simplifying x + -4.34375 = -4.68968699 Reorder the terms: -4.34375 + x = -4.68968699 Solving -4.34375 + x = -4.68968699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.34375' to each side of the equation. -4.34375 + 4.34375 + x = -4.68968699 + 4.34375 Combine like terms: -4.34375 + 4.34375 = 0.00000 0.00000 + x = -4.68968699 + 4.34375 x = -4.68968699 + 4.34375 Combine like terms: -4.68968699 + 4.34375 = -0.34593699 x = -0.34593699 Simplifying x = -0.34593699Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.03343699, -0.34593699}
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