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Simplifying 8x2 + 4x = 63 Reorder the terms: 4x + 8x2 = 63 Solving 4x + 8x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + 4x + 8x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -7.875 + 0.5x + x2 = 0 Move the constant term to the right: Add '7.875' to each side of the equation. -7.875 + 0.5x + 7.875 + x2 = 0 + 7.875 Reorder the terms: -7.875 + 7.875 + 0.5x + x2 = 0 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + 0.5x + x2 = 0 + 7.875 0.5x + x2 = 0 + 7.875 Combine like terms: 0 + 7.875 = 7.875 0.5x + x2 = 7.875 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 7.875 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 7.875 + 0.0625 Combine like terms: 7.875 + 0.0625 = 7.9375 0.0625 + 0.5x + x2 = 7.9375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 7.9375 Calculate the square root of the right side: 2.817356917 Break this problem into two subproblems by setting (x + 0.25) equal to 2.817356917 and -2.817356917.Subproblem 1
x + 0.25 = 2.817356917 Simplifying x + 0.25 = 2.817356917 Reorder the terms: 0.25 + x = 2.817356917 Solving 0.25 + x = 2.817356917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.817356917 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.817356917 + -0.25 x = 2.817356917 + -0.25 Combine like terms: 2.817356917 + -0.25 = 2.567356917 x = 2.567356917 Simplifying x = 2.567356917Subproblem 2
x + 0.25 = -2.817356917 Simplifying x + 0.25 = -2.817356917 Reorder the terms: 0.25 + x = -2.817356917 Solving 0.25 + x = -2.817356917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.817356917 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.817356917 + -0.25 x = -2.817356917 + -0.25 Combine like terms: -2.817356917 + -0.25 = -3.067356917 x = -3.067356917 Simplifying x = -3.067356917Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.567356917, -3.067356917}
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