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Simplifying 7x2 + -10x + 8 + -5x + -13x2 = 0 Reorder the terms: 8 + -10x + -5x + 7x2 + -13x2 = 0 Combine like terms: -10x + -5x = -15x 8 + -15x + 7x2 + -13x2 = 0 Combine like terms: 7x2 + -13x2 = -6x2 8 + -15x + -6x2 = 0 Solving 8 + -15x + -6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.333333333 + 2.5x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 2.5x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 2.5x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 2.5x + x2 = 0 + 1.333333333 2.5x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 2.5x + x2 = 1.333333333 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 1.333333333 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 1.333333333 + 1.5625 Combine like terms: 1.333333333 + 1.5625 = 2.895833333 1.5625 + 2.5x + x2 = 2.895833333 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.895833333 Calculate the square root of the right side: 1.701714821 Break this problem into two subproblems by setting (x + 1.25) equal to 1.701714821 and -1.701714821.Subproblem 1
x + 1.25 = 1.701714821 Simplifying x + 1.25 = 1.701714821 Reorder the terms: 1.25 + x = 1.701714821 Solving 1.25 + x = 1.701714821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.701714821 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.701714821 + -1.25 x = 1.701714821 + -1.25 Combine like terms: 1.701714821 + -1.25 = 0.451714821 x = 0.451714821 Simplifying x = 0.451714821Subproblem 2
x + 1.25 = -1.701714821 Simplifying x + 1.25 = -1.701714821 Reorder the terms: 1.25 + x = -1.701714821 Solving 1.25 + x = -1.701714821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.701714821 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.701714821 + -1.25 x = -1.701714821 + -1.25 Combine like terms: -1.701714821 + -1.25 = -2.951714821 x = -2.951714821 Simplifying x = -2.951714821Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.451714821, -2.951714821}
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