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Simplifying -16x2 + 64x + 190 = 0 Reorder the terms: 190 + 64x + -16x2 = 0 Solving 190 + 64x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(95 + 32x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(95 + 32x + -8x2)' equal to zero and attempt to solve: Simplifying 95 + 32x + -8x2 = 0 Solving 95 + 32x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -11.875 + -4x + x2 = 0 Move the constant term to the right: Add '11.875' to each side of the equation. -11.875 + -4x + 11.875 + x2 = 0 + 11.875 Reorder the terms: -11.875 + 11.875 + -4x + x2 = 0 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + -4x + x2 = 0 + 11.875 -4x + x2 = 0 + 11.875 Combine like terms: 0 + 11.875 = 11.875 -4x + x2 = 11.875 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 11.875 + 4 Reorder the terms: 4 + -4x + x2 = 11.875 + 4 Combine like terms: 11.875 + 4 = 15.875 4 + -4x + x2 = 15.875 Factor a perfect square on the left side: (x + -2)(x + -2) = 15.875 Calculate the square root of the right side: 3.984344363 Break this problem into two subproblems by setting (x + -2) equal to 3.984344363 and -3.984344363.Subproblem 1
x + -2 = 3.984344363 Simplifying x + -2 = 3.984344363 Reorder the terms: -2 + x = 3.984344363 Solving -2 + x = 3.984344363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.984344363 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.984344363 + 2 x = 3.984344363 + 2 Combine like terms: 3.984344363 + 2 = 5.984344363 x = 5.984344363 Simplifying x = 5.984344363Subproblem 2
x + -2 = -3.984344363 Simplifying x + -2 = -3.984344363 Reorder the terms: -2 + x = -3.984344363 Solving -2 + x = -3.984344363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.984344363 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.984344363 + 2 x = -3.984344363 + 2 Combine like terms: -3.984344363 + 2 = -1.984344363 x = -1.984344363 Simplifying x = -1.984344363Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.984344363, -1.984344363}Solution
x = {5.984344363, -1.984344363}
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