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Simplifying (15x2 + -5x + 2) + -4(3x2 + 6x + -7) = 0 Reorder the terms: (2 + -5x + 15x2) + -4(3x2 + 6x + -7) = 0 Remove parenthesis around (2 + -5x + 15x2) 2 + -5x + 15x2 + -4(3x2 + 6x + -7) = 0 Reorder the terms: 2 + -5x + 15x2 + -4(-7 + 6x + 3x2) = 0 2 + -5x + 15x2 + (-7 * -4 + 6x * -4 + 3x2 * -4) = 0 2 + -5x + 15x2 + (28 + -24x + -12x2) = 0 Reorder the terms: 2 + 28 + -5x + -24x + 15x2 + -12x2 = 0 Combine like terms: 2 + 28 = 30 30 + -5x + -24x + 15x2 + -12x2 = 0 Combine like terms: -5x + -24x = -29x 30 + -29x + 15x2 + -12x2 = 0 Combine like terms: 15x2 + -12x2 = 3x2 30 + -29x + 3x2 = 0 Solving 30 + -29x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + -9.666666667x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -9.666666667x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -9.666666667x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -9.666666667x + x2 = 0 + -10 -9.666666667x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -9.666666667x + x2 = -10 The x term is -9.666666667x. Take half its coefficient (-4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. -9.666666667x + 23.36111112 + x2 = -10 + 23.36111112 Reorder the terms: 23.36111112 + -9.666666667x + x2 = -10 + 23.36111112 Combine like terms: -10 + 23.36111112 = 13.36111112 23.36111112 + -9.666666667x + x2 = 13.36111112 Factor a perfect square on the left side: (x + -4.833333334)(x + -4.833333334) = 13.36111112 Calculate the square root of the right side: 3.655285368 Break this problem into two subproblems by setting (x + -4.833333334) equal to 3.655285368 and -3.655285368.Subproblem 1
x + -4.833333334 = 3.655285368 Simplifying x + -4.833333334 = 3.655285368 Reorder the terms: -4.833333334 + x = 3.655285368 Solving -4.833333334 + x = 3.655285368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = 3.655285368 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = 3.655285368 + 4.833333334 x = 3.655285368 + 4.833333334 Combine like terms: 3.655285368 + 4.833333334 = 8.488618702 x = 8.488618702 Simplifying x = 8.488618702Subproblem 2
x + -4.833333334 = -3.655285368 Simplifying x + -4.833333334 = -3.655285368 Reorder the terms: -4.833333334 + x = -3.655285368 Solving -4.833333334 + x = -3.655285368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = -3.655285368 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = -3.655285368 + 4.833333334 x = -3.655285368 + 4.833333334 Combine like terms: -3.655285368 + 4.833333334 = 1.178047966 x = 1.178047966 Simplifying x = 1.178047966Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.488618702, 1.178047966}
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