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Simplifying 4x2 + -1x + -225 = 0 Reorder the terms: -225 + -1x + 4x2 = 0 Solving -225 + -1x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -56.25 + -0.25x + x2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + -0.25x + 56.25 + x2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + -0.25x + x2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + -0.25x + x2 = 0 + 56.25 -0.25x + x2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 -0.25x + x2 = 56.25 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 56.25 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 56.25 + 0.015625 Combine like terms: 56.25 + 0.015625 = 56.265625 0.015625 + -0.25x + x2 = 56.265625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 56.265625 Calculate the square root of the right side: 7.501041594 Break this problem into two subproblems by setting (x + -0.125) equal to 7.501041594 and -7.501041594.Subproblem 1
x + -0.125 = 7.501041594 Simplifying x + -0.125 = 7.501041594 Reorder the terms: -0.125 + x = 7.501041594 Solving -0.125 + x = 7.501041594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 7.501041594 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 7.501041594 + 0.125 x = 7.501041594 + 0.125 Combine like terms: 7.501041594 + 0.125 = 7.626041594 x = 7.626041594 Simplifying x = 7.626041594Subproblem 2
x + -0.125 = -7.501041594 Simplifying x + -0.125 = -7.501041594 Reorder the terms: -0.125 + x = -7.501041594 Solving -0.125 + x = -7.501041594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -7.501041594 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -7.501041594 + 0.125 x = -7.501041594 + 0.125 Combine like terms: -7.501041594 + 0.125 = -7.376041594 x = -7.376041594 Simplifying x = -7.376041594Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.626041594, -7.376041594}
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