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Simplifying -3x(2x + -5) = 7 + -4x Reorder the terms: -3x(-5 + 2x) = 7 + -4x (-5 * -3x + 2x * -3x) = 7 + -4x (15x + -6x2) = 7 + -4x Solving 15x + -6x2 = 7 + -4x Solving for variable 'x'. Reorder the terms: -7 + 15x + 4x + -6x2 = 7 + -4x + -7 + 4x Combine like terms: 15x + 4x = 19x -7 + 19x + -6x2 = 7 + -4x + -7 + 4x Reorder the terms: -7 + 19x + -6x2 = 7 + -7 + -4x + 4x Combine like terms: 7 + -7 = 0 -7 + 19x + -6x2 = 0 + -4x + 4x -7 + 19x + -6x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -7 + 19x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 1.166666667 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + -3.166666667x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + -3.166666667x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + -1.166666667 -3.166666667x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 -3.166666667x + x2 = -1.166666667 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = -1.166666667 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = -1.166666667 + 2.506944447 Combine like terms: -1.166666667 + 2.506944447 = 1.34027778 2.506944447 + -3.166666667x + x2 = 1.34027778 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 1.34027778 Calculate the square root of the right side: 1.157703667 Break this problem into two subproblems by setting (x + -1.583333334) equal to 1.157703667 and -1.157703667.Subproblem 1
x + -1.583333334 = 1.157703667 Simplifying x + -1.583333334 = 1.157703667 Reorder the terms: -1.583333334 + x = 1.157703667 Solving -1.583333334 + x = 1.157703667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 1.157703667 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 1.157703667 + 1.583333334 x = 1.157703667 + 1.583333334 Combine like terms: 1.157703667 + 1.583333334 = 2.741037001 x = 2.741037001 Simplifying x = 2.741037001Subproblem 2
x + -1.583333334 = -1.157703667 Simplifying x + -1.583333334 = -1.157703667 Reorder the terms: -1.583333334 + x = -1.157703667 Solving -1.583333334 + x = -1.157703667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -1.157703667 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -1.157703667 + 1.583333334 x = -1.157703667 + 1.583333334 Combine like terms: -1.157703667 + 1.583333334 = 0.425629667 x = 0.425629667 Simplifying x = 0.425629667Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.741037001, 0.425629667}
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