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Simplifying 2(x2 + -4x + 5) + -1(x2 + 6x + -1) = 0 Reorder the terms: 2(5 + -4x + x2) + -1(x2 + 6x + -1) = 0 (5 * 2 + -4x * 2 + x2 * 2) + -1(x2 + 6x + -1) = 0 (10 + -8x + 2x2) + -1(x2 + 6x + -1) = 0 Reorder the terms: 10 + -8x + 2x2 + -1(-1 + 6x + x2) = 0 10 + -8x + 2x2 + (-1 * -1 + 6x * -1 + x2 * -1) = 0 10 + -8x + 2x2 + (1 + -6x + -1x2) = 0 Reorder the terms: 10 + 1 + -8x + -6x + 2x2 + -1x2 = 0 Combine like terms: 10 + 1 = 11 11 + -8x + -6x + 2x2 + -1x2 = 0 Combine like terms: -8x + -6x = -14x 11 + -14x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 11 + -14x + 1x2 = 0 Solving 11 + -14x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -14x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -14x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -14x + x2 = 0 + -11 -14x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -14x + x2 = -11 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -11 + 49 Reorder the terms: 49 + -14x + x2 = -11 + 49 Combine like terms: -11 + 49 = 38 49 + -14x + x2 = 38 Factor a perfect square on the left side: (x + -7)(x + -7) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + -7) equal to 6.164414003 and -6.164414003.Subproblem 1
x + -7 = 6.164414003 Simplifying x + -7 = 6.164414003 Reorder the terms: -7 + x = 6.164414003 Solving -7 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 6.164414003 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.164414003 + 7 x = 6.164414003 + 7 Combine like terms: 6.164414003 + 7 = 13.164414003 x = 13.164414003 Simplifying x = 13.164414003Subproblem 2
x + -7 = -6.164414003 Simplifying x + -7 = -6.164414003 Reorder the terms: -7 + x = -6.164414003 Solving -7 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -6.164414003 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.164414003 + 7 x = -6.164414003 + 7 Combine like terms: -6.164414003 + 7 = 0.835585997 x = 0.835585997 Simplifying x = 0.835585997Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.164414003, 0.835585997}
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