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Simplifying 10x2 + 16x + -2 = 0 Reorder the terms: -2 + 16x + 10x2 = 0 Solving -2 + 16x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 8x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 8x + 5x2)' equal to zero and attempt to solve: Simplifying -1 + 8x + 5x2 = 0 Solving -1 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 1.6x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 1.6x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 1.6x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 1.6x + x2 = 0 + 0.2 1.6x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 1.6x + x2 = 0.2 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 0.2 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 0.2 + 0.64 Combine like terms: 0.2 + 0.64 = 0.84 0.64 + 1.6x + x2 = 0.84 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + 0.8) equal to 0.916515139 and -0.916515139.Subproblem 1
x + 0.8 = 0.916515139 Simplifying x + 0.8 = 0.916515139 Reorder the terms: 0.8 + x = 0.916515139 Solving 0.8 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 0.916515139 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 0.916515139 + -0.8 x = 0.916515139 + -0.8 Combine like terms: 0.916515139 + -0.8 = 0.116515139 x = 0.116515139 Simplifying x = 0.116515139Subproblem 2
x + 0.8 = -0.916515139 Simplifying x + 0.8 = -0.916515139 Reorder the terms: 0.8 + x = -0.916515139 Solving 0.8 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -0.916515139 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -0.916515139 + -0.8 x = -0.916515139 + -0.8 Combine like terms: -0.916515139 + -0.8 = -1.716515139 x = -1.716515139 Simplifying x = -1.716515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.116515139, -1.716515139}Solution
x = {0.116515139, -1.716515139}
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