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Simplifying -8x2 + -10x + 10 = 0 Reorder the terms: 10 + -10x + -8x2 = 0 Solving 10 + -10x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -5x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -5x + -4x2)' equal to zero and attempt to solve: Simplifying 5 + -5x + -4x2 = 0 Solving 5 + -5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.25x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.25x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.25x + x2 = 0 + 1.25 1.25x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.25x + x2 = 1.25 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 = 1.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 1.25 + 0.390625 Combine like terms: 1.25 + 0.390625 = 1.640625 0.390625 + 1.25x + x2 = 1.640625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 0.625) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 0.625 = 1.280868846 Simplifying x + 0.625 = 1.280868846 Reorder the terms: 0.625 + x = 1.280868846 Solving 0.625 + x = 1.280868846 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 = 1.280868846 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.280868846 + -0.625 x = 1.280868846 + -0.625 Combine like terms: 1.280868846 + -0.625 = 0.655868846 x = 0.655868846 Simplifying x = 0.655868846Subproblem 2
x + 0.625 = -1.280868846 Simplifying x + 0.625 = -1.280868846 Reorder the terms: 0.625 + x = -1.280868846 Solving 0.625 + x = -1.280868846 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 = -1.280868846 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.280868846 + -0.625 x = -1.280868846 + -0.625 Combine like terms: -1.280868846 + -0.625 = -1.905868846 x = -1.905868846 Simplifying x = -1.905868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.655868846, -1.905868846}Solution
x = {0.655868846, -1.905868846}
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