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Simplifying 10x2 + -64x + -30 = 0 Reorder the terms: -30 + -64x + 10x2 = 0 Solving -30 + -64x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -32x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -32x + 5x2)' equal to zero and attempt to solve: Simplifying -15 + -32x + 5x2 = 0 Solving -15 + -32x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + -6.4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -6.4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -6.4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6.4x + x2 = 0 + 3 -6.4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6.4x + x2 = 3 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = 3 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = 3 + 10.24 Combine like terms: 3 + 10.24 = 13.24 10.24 + -6.4x + x2 = 13.24 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 13.24 Calculate the square root of the right side: 3.63868108 Break this problem into two subproblems by setting (x + -3.2) equal to 3.63868108 and -3.63868108.Subproblem 1
x + -3.2 = 3.63868108 Simplifying x + -3.2 = 3.63868108 Reorder the terms: -3.2 + x = 3.63868108 Solving -3.2 + x = 3.63868108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 3.63868108 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 3.63868108 + 3.2 x = 3.63868108 + 3.2 Combine like terms: 3.63868108 + 3.2 = 6.83868108 x = 6.83868108 Simplifying x = 6.83868108Subproblem 2
x + -3.2 = -3.63868108 Simplifying x + -3.2 = -3.63868108 Reorder the terms: -3.2 + x = -3.63868108 Solving -3.2 + x = -3.63868108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -3.63868108 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -3.63868108 + 3.2 x = -3.63868108 + 3.2 Combine like terms: -3.63868108 + 3.2 = -0.43868108 x = -0.43868108 Simplifying x = -0.43868108Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.83868108, -0.43868108}Solution
x = {6.83868108, -0.43868108}
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