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Simplifying -0.5x2 + 5.25x + -5 = 0 Reorder the terms: -5 + 5.25x + -0.5x2 = 0 Solving -5 + 5.25x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 10 + -10.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -10.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10.5x + x2 = 0 + -10 -10.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -10.5x + x2 = -10 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -10 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -10 + 27.5625 Combine like terms: -10 + 27.5625 = 17.5625 27.5625 + -10.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + -5.25) equal to 4.190763654 and -4.190763654.Subproblem 1
x + -5.25 = 4.190763654 Simplifying x + -5.25 = 4.190763654 Reorder the terms: -5.25 + x = 4.190763654 Solving -5.25 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.190763654 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.190763654 + 5.25 x = 4.190763654 + 5.25 Combine like terms: 4.190763654 + 5.25 = 9.440763654 x = 9.440763654 Simplifying x = 9.440763654Subproblem 2
x + -5.25 = -4.190763654 Simplifying x + -5.25 = -4.190763654 Reorder the terms: -5.25 + x = -4.190763654 Solving -5.25 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.190763654 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.190763654 + 5.25 x = -4.190763654 + 5.25 Combine like terms: -4.190763654 + 5.25 = 1.059236346 x = 1.059236346 Simplifying x = 1.059236346Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.440763654, 1.059236346}
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