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Simplifying 8x = 5x2 + -1 Reorder the terms: 8x = -1 + 5x2 Solving 8x = -1 + 5x2 Solving for variable 'x'. Reorder the terms: 1 + 8x + -5x2 = -1 + 5x2 + 1 + -5x2 Reorder the terms: 1 + 8x + -5x2 = -1 + 1 + 5x2 + -5x2 Combine like terms: -1 + 1 = 0 1 + 8x + -5x2 = 0 + 5x2 + -5x2 1 + 8x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 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 = 1.716515139 x = 1.716515139 Simplifying x = 1.716515139Subproblem 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 = -0.116515139 x = -0.116515139 Simplifying x = -0.116515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.716515139, -0.116515139}
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