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Simplifying 3x(x + -4) = 5x + -7 Reorder the terms: 3x(-4 + x) = 5x + -7 (-4 * 3x + x * 3x) = 5x + -7 (-12x + 3x2) = 5x + -7 Reorder the terms: -12x + 3x2 = -7 + 5x Solving -12x + 3x2 = -7 + 5x Solving for variable 'x'. Reorder the terms: 7 + -12x + -5x + 3x2 = -7 + 5x + 7 + -5x Combine like terms: -12x + -5x = -17x 7 + -17x + 3x2 = -7 + 5x + 7 + -5x Reorder the terms: 7 + -17x + 3x2 = -7 + 7 + 5x + -5x Combine like terms: -7 + 7 = 0 7 + -17x + 3x2 = 0 + 5x + -5x 7 + -17x + 3x2 = 5x + -5x Combine like terms: 5x + -5x = 0 7 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -5.666666667x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -5.666666667x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -5.666666667x + x2 = 0 + -2.333333333 -5.666666667x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -5.666666667x + x2 = -2.333333333 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = -2.333333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = -2.333333333 + 8.027777782 Combine like terms: -2.333333333 + 8.027777782 = 5.694444449 8.027777782 + -5.666666667x + x2 = 5.694444449 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 5.694444449 Calculate the square root of the right side: 2.386303512 Break this problem into two subproblems by setting (x + -2.833333334) equal to 2.386303512 and -2.386303512.Subproblem 1
x + -2.833333334 = 2.386303512 Simplifying x + -2.833333334 = 2.386303512 Reorder the terms: -2.833333334 + x = 2.386303512 Solving -2.833333334 + x = 2.386303512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 2.386303512 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 2.386303512 + 2.833333334 x = 2.386303512 + 2.833333334 Combine like terms: 2.386303512 + 2.833333334 = 5.219636846 x = 5.219636846 Simplifying x = 5.219636846Subproblem 2
x + -2.833333334 = -2.386303512 Simplifying x + -2.833333334 = -2.386303512 Reorder the terms: -2.833333334 + x = -2.386303512 Solving -2.833333334 + x = -2.386303512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -2.386303512 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -2.386303512 + 2.833333334 x = -2.386303512 + 2.833333334 Combine like terms: -2.386303512 + 2.833333334 = 0.447029822 x = 0.447029822 Simplifying x = 0.447029822Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.219636846, 0.447029822}
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