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Simplifying 4(3x + -1) + (2x + 3)(x + -7) = 0 Reorder the terms: 4(-1 + 3x) + (2x + 3)(x + -7) = 0 (-1 * 4 + 3x * 4) + (2x + 3)(x + -7) = 0 (-4 + 12x) + (2x + 3)(x + -7) = 0 Reorder the terms: -4 + 12x + (3 + 2x)(x + -7) = 0 Reorder the terms: -4 + 12x + (3 + 2x)(-7 + x) = 0 Multiply (3 + 2x) * (-7 + x) -4 + 12x + (3(-7 + x) + 2x * (-7 + x)) = 0 -4 + 12x + ((-7 * 3 + x * 3) + 2x * (-7 + x)) = 0 -4 + 12x + ((-21 + 3x) + 2x * (-7 + x)) = 0 -4 + 12x + (-21 + 3x + (-7 * 2x + x * 2x)) = 0 -4 + 12x + (-21 + 3x + (-14x + 2x2)) = 0 Combine like terms: 3x + -14x = -11x -4 + 12x + (-21 + -11x + 2x2) = 0 Reorder the terms: -4 + -21 + 12x + -11x + 2x2 = 0 Combine like terms: -4 + -21 = -25 -25 + 12x + -11x + 2x2 = 0 Combine like terms: 12x + -11x = 1x -25 + 1x + 2x2 = 0 Solving -25 + 1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 0.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 0.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 0.5x + x2 = 0 + 12.5 0.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 0.5x + x2 = 12.5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 12.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 12.5 + 0.0625 Combine like terms: 12.5 + 0.0625 = 12.5625 0.0625 + 0.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 0.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 0.25 = 3.54436172 Simplifying x + 0.25 = 3.54436172 Reorder the terms: 0.25 + x = 3.54436172 Solving 0.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.54436172 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.54436172 + -0.25 x = 3.54436172 + -0.25 Combine like terms: 3.54436172 + -0.25 = 3.29436172 x = 3.29436172 Simplifying x = 3.29436172Subproblem 2
x + 0.25 = -3.54436172 Simplifying x + 0.25 = -3.54436172 Reorder the terms: 0.25 + x = -3.54436172 Solving 0.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.54436172 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.54436172 + -0.25 x = -3.54436172 + -0.25 Combine like terms: -3.54436172 + -0.25 = -3.79436172 x = -3.79436172 Simplifying x = -3.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.29436172, -3.79436172}
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