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Simplifying 7x2 + -5x + -45 = 0 Reorder the terms: -45 + -5x + 7x2 = 0 Solving -45 + -5x + 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'. -6.428571429 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '6.428571429' to each side of the equation. -6.428571429 + -0.7142857143x + 6.428571429 + x2 = 0 + 6.428571429 Reorder the terms: -6.428571429 + 6.428571429 + -0.7142857143x + x2 = 0 + 6.428571429 Combine like terms: -6.428571429 + 6.428571429 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 6.428571429 -0.7142857143x + x2 = 0 + 6.428571429 Combine like terms: 0 + 6.428571429 = 6.428571429 -0.7142857143x + x2 = 6.428571429 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 6.428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 6.428571429 + 0.1275510204 Combine like terms: 6.428571429 + 0.1275510204 = 6.5561224494 0.1275510204 + -0.7142857143x + x2 = 6.5561224494 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 6.5561224494 Calculate the square root of the right side: 2.560492619 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 2.560492619 and -2.560492619.Subproblem 1
x + -0.3571428572 = 2.560492619 Simplifying x + -0.3571428572 = 2.560492619 Reorder the terms: -0.3571428572 + x = 2.560492619 Solving -0.3571428572 + x = 2.560492619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 2.560492619 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 2.560492619 + 0.3571428572 x = 2.560492619 + 0.3571428572 Combine like terms: 2.560492619 + 0.3571428572 = 2.9176354762 x = 2.9176354762 Simplifying x = 2.9176354762Subproblem 2
x + -0.3571428572 = -2.560492619 Simplifying x + -0.3571428572 = -2.560492619 Reorder the terms: -0.3571428572 + x = -2.560492619 Solving -0.3571428572 + x = -2.560492619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -2.560492619 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -2.560492619 + 0.3571428572 x = -2.560492619 + 0.3571428572 Combine like terms: -2.560492619 + 0.3571428572 = -2.2033497618 x = -2.2033497618 Simplifying x = -2.2033497618Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9176354762, -2.2033497618}
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