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Simplifying 7x2 + -256x + -225 = 0 Reorder the terms: -225 + -256x + 7x2 = 0 Solving -225 + -256x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -32.14285714 + -36.57142857x + x2 = 0 Move the constant term to the right: Add '32.14285714' to each side of the equation. -32.14285714 + -36.57142857x + 32.14285714 + x2 = 0 + 32.14285714 Reorder the terms: -32.14285714 + 32.14285714 + -36.57142857x + x2 = 0 + 32.14285714 Combine like terms: -32.14285714 + 32.14285714 = 0.00000000 0.00000000 + -36.57142857x + x2 = 0 + 32.14285714 -36.57142857x + x2 = 0 + 32.14285714 Combine like terms: 0 + 32.14285714 = 32.14285714 -36.57142857x + x2 = 32.14285714 The x term is -36.57142857x. Take half its coefficient (-18.28571429). Square it (334.3673471) and add it to both sides. Add '334.3673471' to each side of the equation. -36.57142857x + 334.3673471 + x2 = 32.14285714 + 334.3673471 Reorder the terms: 334.3673471 + -36.57142857x + x2 = 32.14285714 + 334.3673471 Combine like terms: 32.14285714 + 334.3673471 = 366.51020424 334.3673471 + -36.57142857x + x2 = 366.51020424 Factor a perfect square on the left side: (x + -18.28571429)(x + -18.28571429) = 366.51020424 Calculate the square root of the right side: 19.144456227 Break this problem into two subproblems by setting (x + -18.28571429) equal to 19.144456227 and -19.144456227.Subproblem 1
x + -18.28571429 = 19.144456227 Simplifying x + -18.28571429 = 19.144456227 Reorder the terms: -18.28571429 + x = 19.144456227 Solving -18.28571429 + x = 19.144456227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.28571429' to each side of the equation. -18.28571429 + 18.28571429 + x = 19.144456227 + 18.28571429 Combine like terms: -18.28571429 + 18.28571429 = 0.00000000 0.00000000 + x = 19.144456227 + 18.28571429 x = 19.144456227 + 18.28571429 Combine like terms: 19.144456227 + 18.28571429 = 37.430170517 x = 37.430170517 Simplifying x = 37.430170517Subproblem 2
x + -18.28571429 = -19.144456227 Simplifying x + -18.28571429 = -19.144456227 Reorder the terms: -18.28571429 + x = -19.144456227 Solving -18.28571429 + x = -19.144456227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.28571429' to each side of the equation. -18.28571429 + 18.28571429 + x = -19.144456227 + 18.28571429 Combine like terms: -18.28571429 + 18.28571429 = 0.00000000 0.00000000 + x = -19.144456227 + 18.28571429 x = -19.144456227 + 18.28571429 Combine like terms: -19.144456227 + 18.28571429 = -0.858741937 x = -0.858741937 Simplifying x = -0.858741937Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.430170517, -0.858741937}
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