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Simplifying -4(-2x + -7) * 6x + -7 = 0 Reorder the terms: -4(-7 + -2x) * 6x + -7 = 0 Reorder the terms for easier multiplication: -4 * 6x(-7 + -2x) + -7 = 0 Multiply -4 * 6 -24x(-7 + -2x) + -7 = 0 (-7 * -24x + -2x * -24x) + -7 = 0 (168x + 48x2) + -7 = 0 Reorder the terms: -7 + 168x + 48x2 = 0 Solving -7 + 168x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.1458333333 + 3.5x + x2 = 0 Move the constant term to the right: Add '0.1458333333' to each side of the equation. -0.1458333333 + 3.5x + 0.1458333333 + x2 = 0 + 0.1458333333 Reorder the terms: -0.1458333333 + 0.1458333333 + 3.5x + x2 = 0 + 0.1458333333 Combine like terms: -0.1458333333 + 0.1458333333 = 0.0000000000 0.0000000000 + 3.5x + x2 = 0 + 0.1458333333 3.5x + x2 = 0 + 0.1458333333 Combine like terms: 0 + 0.1458333333 = 0.1458333333 3.5x + x2 = 0.1458333333 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 0.1458333333 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 0.1458333333 + 3.0625 Combine like terms: 0.1458333333 + 3.0625 = 3.2083333333 3.0625 + 3.5x + x2 = 3.2083333333 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 3.2083333333 Calculate the square root of the right side: 1.791182105 Break this problem into two subproblems by setting (x + 1.75) equal to 1.791182105 and -1.791182105.Subproblem 1
x + 1.75 = 1.791182105 Simplifying x + 1.75 = 1.791182105 Reorder the terms: 1.75 + x = 1.791182105 Solving 1.75 + x = 1.791182105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.791182105 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.791182105 + -1.75 x = 1.791182105 + -1.75 Combine like terms: 1.791182105 + -1.75 = 0.041182105 x = 0.041182105 Simplifying x = 0.041182105Subproblem 2
x + 1.75 = -1.791182105 Simplifying x + 1.75 = -1.791182105 Reorder the terms: 1.75 + x = -1.791182105 Solving 1.75 + x = -1.791182105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.791182105 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.791182105 + -1.75 x = -1.791182105 + -1.75 Combine like terms: -1.791182105 + -1.75 = -3.541182105 x = -3.541182105 Simplifying x = -3.541182105Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.041182105, -3.541182105}
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