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Simplifying -9x2 + -14x + -5x2 + 2 + 15x = 0 Reorder the terms: 2 + -14x + 15x + -9x2 + -5x2 = 0 Combine like terms: -14x + 15x = 1x 2 + 1x + -9x2 + -5x2 = 0 Combine like terms: -9x2 + -5x2 = -14x2 2 + 1x + -14x2 = 0 Solving 2 + 1x + -14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.1428571429 + -0.07142857143x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.07142857143x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.07142857143x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.07142857143x + x2 = 0 + 0.1428571429 -0.07142857143x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.07142857143x + x2 = 0.1428571429 The x term is -0.07142857143x. Take half its coefficient (-0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. -0.07142857143x + 0.001275510204 + x2 = 0.1428571429 + 0.001275510204 Reorder the terms: 0.001275510204 + -0.07142857143x + x2 = 0.1428571429 + 0.001275510204 Combine like terms: 0.1428571429 + 0.001275510204 = 0.144132653104 0.001275510204 + -0.07142857143x + x2 = 0.144132653104 Factor a perfect square on the left side: (x + -0.03571428572)(x + -0.03571428572) = 0.144132653104 Calculate the square root of the right side: 0.379648065 Break this problem into two subproblems by setting (x + -0.03571428572) equal to 0.379648065 and -0.379648065.Subproblem 1
x + -0.03571428572 = 0.379648065 Simplifying x + -0.03571428572 = 0.379648065 Reorder the terms: -0.03571428572 + x = 0.379648065 Solving -0.03571428572 + x = 0.379648065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03571428572' to each side of the equation. -0.03571428572 + 0.03571428572 + x = 0.379648065 + 0.03571428572 Combine like terms: -0.03571428572 + 0.03571428572 = 0.00000000000 0.00000000000 + x = 0.379648065 + 0.03571428572 x = 0.379648065 + 0.03571428572 Combine like terms: 0.379648065 + 0.03571428572 = 0.41536235072 x = 0.41536235072 Simplifying x = 0.41536235072Subproblem 2
x + -0.03571428572 = -0.379648065 Simplifying x + -0.03571428572 = -0.379648065 Reorder the terms: -0.03571428572 + x = -0.379648065 Solving -0.03571428572 + x = -0.379648065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03571428572' to each side of the equation. -0.03571428572 + 0.03571428572 + x = -0.379648065 + 0.03571428572 Combine like terms: -0.03571428572 + 0.03571428572 = 0.00000000000 0.00000000000 + x = -0.379648065 + 0.03571428572 x = -0.379648065 + 0.03571428572 Combine like terms: -0.379648065 + 0.03571428572 = -0.34393377928 x = -0.34393377928 Simplifying x = -0.34393377928Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.41536235072, -0.34393377928}
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