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Simplifying 2x2 + 64x + -190 = 0 Reorder the terms: -190 + 64x + 2x2 = 0 Solving -190 + 64x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + 32x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + 32x + x2)' equal to zero and attempt to solve: Simplifying -95 + 32x + x2 = 0 Solving -95 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + 32x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + 32x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 32x + x2 = 0 + 95 32x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 32x + x2 = 95 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 95 + 256 Reorder the terms: 256 + 32x + x2 = 95 + 256 Combine like terms: 95 + 256 = 351 256 + 32x + x2 = 351 Factor a perfect square on the left side: (x + 16)(x + 16) = 351 Calculate the square root of the right side: 18.734993995 Break this problem into two subproblems by setting (x + 16) equal to 18.734993995 and -18.734993995.Subproblem 1
x + 16 = 18.734993995 Simplifying x + 16 = 18.734993995 Reorder the terms: 16 + x = 18.734993995 Solving 16 + x = 18.734993995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 18.734993995 + -16 Combine like terms: 16 + -16 = 0 0 + x = 18.734993995 + -16 x = 18.734993995 + -16 Combine like terms: 18.734993995 + -16 = 2.734993995 x = 2.734993995 Simplifying x = 2.734993995Subproblem 2
x + 16 = -18.734993995 Simplifying x + 16 = -18.734993995 Reorder the terms: 16 + x = -18.734993995 Solving 16 + x = -18.734993995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -18.734993995 + -16 Combine like terms: 16 + -16 = 0 0 + x = -18.734993995 + -16 x = -18.734993995 + -16 Combine like terms: -18.734993995 + -16 = -34.734993995 x = -34.734993995 Simplifying x = -34.734993995Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.734993995, -34.734993995}Solution
x = {2.734993995, -34.734993995}
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