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Simplifying -8x2 + 10x + 8 = 0 Reorder the terms: 8 + 10x + -8x2 = 0 Solving 8 + 10x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 5x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 5x + -4x2)' equal to zero and attempt to solve: Simplifying 4 + 5x + -4x2 = 0 Solving 4 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1 + -1.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.25x + x2 = 0 + 1 -1.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.25x + x2 = 1 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 1 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 1 + 0.390625 Combine like terms: 1 + 0.390625 = 1.390625 0.390625 + -1.25x + x2 = 1.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + -0.625) equal to 1.179247642 and -1.179247642.Subproblem 1
x + -0.625 = 1.179247642 Simplifying x + -0.625 = 1.179247642 Reorder the terms: -0.625 + x = 1.179247642 Solving -0.625 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.179247642 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.179247642 + 0.625 x = 1.179247642 + 0.625 Combine like terms: 1.179247642 + 0.625 = 1.804247642 x = 1.804247642 Simplifying x = 1.804247642Subproblem 2
x + -0.625 = -1.179247642 Simplifying x + -0.625 = -1.179247642 Reorder the terms: -0.625 + x = -1.179247642 Solving -0.625 + x = -1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.179247642 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.179247642 + 0.625 x = -1.179247642 + 0.625 Combine like terms: -1.179247642 + 0.625 = -0.554247642 x = -0.554247642 Simplifying x = -0.554247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.804247642, -0.554247642}Solution
x = {1.804247642, -0.554247642}
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