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Simplifying 1.2x + -0.125x2 + 32 = 0 Reorder the terms: 32 + 1.2x + -0.125x2 = 0 Solving 32 + 1.2x + -0.125x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.125 the coefficient of the squared term: Divide each side by '-0.125'. -256 + -9.6x + x2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + -9.6x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + -9.6x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -9.6x + x2 = 0 + 256 -9.6x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 -9.6x + x2 = 256 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = 256 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = 256 + 23.04 Combine like terms: 256 + 23.04 = 279.04 23.04 + -9.6x + x2 = 279.04 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 279.04 Calculate the square root of the right side: 16.704490414 Break this problem into two subproblems by setting (x + -4.8) equal to 16.704490414 and -16.704490414.Subproblem 1
x + -4.8 = 16.704490414 Simplifying x + -4.8 = 16.704490414 Reorder the terms: -4.8 + x = 16.704490414 Solving -4.8 + x = 16.704490414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 16.704490414 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 16.704490414 + 4.8 x = 16.704490414 + 4.8 Combine like terms: 16.704490414 + 4.8 = 21.504490414 x = 21.504490414 Simplifying x = 21.504490414Subproblem 2
x + -4.8 = -16.704490414 Simplifying x + -4.8 = -16.704490414 Reorder the terms: -4.8 + x = -16.704490414 Solving -4.8 + x = -16.704490414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -16.704490414 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -16.704490414 + 4.8 x = -16.704490414 + 4.8 Combine like terms: -16.704490414 + 4.8 = -11.904490414 x = -11.904490414 Simplifying x = -11.904490414Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.504490414, -11.904490414}
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