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Simplifying (7x * x + -3x + 4) + -1(6x * x + -2x + 7) = 0 Multiply x * x (7x2 + -3x + 4) + -1(6x * x + -2x + 7) = 0 Reorder the terms: (4 + -3x + 7x2) + -1(6x * x + -2x + 7) = 0 Remove parenthesis around (4 + -3x + 7x2) 4 + -3x + 7x2 + -1(6x * x + -2x + 7) = 0 Multiply x * x 4 + -3x + 7x2 + -1(6x2 + -2x + 7) = 0 Reorder the terms: 4 + -3x + 7x2 + -1(7 + -2x + 6x2) = 0 4 + -3x + 7x2 + (7 * -1 + -2x * -1 + 6x2 * -1) = 0 4 + -3x + 7x2 + (-7 + 2x + -6x2) = 0 Reorder the terms: 4 + -7 + -3x + 2x + 7x2 + -6x2 = 0 Combine like terms: 4 + -7 = -3 -3 + -3x + 2x + 7x2 + -6x2 = 0 Combine like terms: -3x + 2x = -1x -3 + -1x + 7x2 + -6x2 = 0 Combine like terms: 7x2 + -6x2 = 1x2 -3 + -1x + 1x2 = 0 Solving -3 + -1x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x + x2 = 0 + 3 -1x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x + x2 = 3 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1x + x2 = 3.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -0.5 = 1.802775638 Simplifying x + -0.5 = 1.802775638 Reorder the terms: -0.5 + x = 1.802775638 Solving -0.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.802775638 + 0.5 x = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 x = 2.302775638 Simplifying x = 2.302775638Subproblem 2
x + -0.5 = -1.802775638 Simplifying x + -0.5 = -1.802775638 Reorder the terms: -0.5 + x = -1.802775638 Solving -0.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.802775638 + 0.5 x = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 x = -1.302775638 Simplifying x = -1.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.302775638, -1.302775638}
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