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Simplifying 0 = 10 + 40x + -16x2 Solving 0 = 10 + 40x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -40x + 16x2 = 10 + 40x + -16x2 + -10 + -40x + 16x2 Reorder the terms: -10 + -40x + 16x2 = 10 + -10 + 40x + -40x + -16x2 + 16x2 Combine like terms: 10 + -10 = 0 -10 + -40x + 16x2 = 0 + 40x + -40x + -16x2 + 16x2 -10 + -40x + 16x2 = 40x + -40x + -16x2 + 16x2 Combine like terms: 40x + -40x = 0 -10 + -40x + 16x2 = 0 + -16x2 + 16x2 -10 + -40x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -10 + -40x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -20x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -20x + 8x2)' equal to zero and attempt to solve: Simplifying -5 + -20x + 8x2 = 0 Solving -5 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -2.5x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -2.5x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -2.5x + x2 = 0 + 0.625 -2.5x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -2.5x + x2 = 0.625 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 0.625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.625 + 1.5625 Combine like terms: 0.625 + 1.5625 = 2.1875 1.5625 + -2.5x + x2 = 2.1875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.1875 Calculate the square root of the right side: 1.479019946 Break this problem into two subproblems by setting (x + -1.25) equal to 1.479019946 and -1.479019946.Subproblem 1
x + -1.25 = 1.479019946 Simplifying x + -1.25 = 1.479019946 Reorder the terms: -1.25 + x = 1.479019946 Solving -1.25 + x = 1.479019946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.479019946 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.479019946 + 1.25 x = 1.479019946 + 1.25 Combine like terms: 1.479019946 + 1.25 = 2.729019946 x = 2.729019946 Simplifying x = 2.729019946Subproblem 2
x + -1.25 = -1.479019946 Simplifying x + -1.25 = -1.479019946 Reorder the terms: -1.25 + x = -1.479019946 Solving -1.25 + x = -1.479019946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.479019946 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.479019946 + 1.25 x = -1.479019946 + 1.25 Combine like terms: -1.479019946 + 1.25 = -0.229019946 x = -0.229019946 Simplifying x = -0.229019946Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.729019946, -0.229019946}Solution
x = {2.729019946, -0.229019946}
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