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Simplifying 0 = -16x2 + 2x + 10 Reorder the terms: 0 = 10 + 2x + -16x2 Solving 0 = 10 + 2x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -2x + 16x2 = 10 + 2x + -16x2 + -10 + -2x + 16x2 Reorder the terms: -10 + -2x + 16x2 = 10 + -10 + 2x + -2x + -16x2 + 16x2 Combine like terms: 10 + -10 = 0 -10 + -2x + 16x2 = 0 + 2x + -2x + -16x2 + 16x2 -10 + -2x + 16x2 = 2x + -2x + -16x2 + 16x2 Combine like terms: 2x + -2x = 0 -10 + -2x + 16x2 = 0 + -16x2 + 16x2 -10 + -2x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -10 + -2x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -1x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1x + 8x2)' equal to zero and attempt to solve: Simplifying -5 + -1x + 8x2 = 0 Solving -5 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.125x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.125x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.125x + x2 = 0 + 0.625 -0.125x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.125x + x2 = 0.625 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 0.625 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.625 + 0.00390625 Combine like terms: 0.625 + 0.00390625 = 0.62890625 0.00390625 + -0.125x + x2 = 0.62890625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.62890625 Calculate the square root of the right side: 0.793036096 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.793036096 and -0.793036096.Subproblem 1
x + -0.0625 = 0.793036096 Simplifying x + -0.0625 = 0.793036096 Reorder the terms: -0.0625 + x = 0.793036096 Solving -0.0625 + x = 0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.793036096 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.793036096 + 0.0625 x = 0.793036096 + 0.0625 Combine like terms: 0.793036096 + 0.0625 = 0.855536096 x = 0.855536096 Simplifying x = 0.855536096Subproblem 2
x + -0.0625 = -0.793036096 Simplifying x + -0.0625 = -0.793036096 Reorder the terms: -0.0625 + x = -0.793036096 Solving -0.0625 + x = -0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.793036096 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.793036096 + 0.0625 x = -0.793036096 + 0.0625 Combine like terms: -0.793036096 + 0.0625 = -0.730536096 x = -0.730536096 Simplifying x = -0.730536096Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.855536096, -0.730536096}Solution
x = {0.855536096, -0.730536096}
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