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Simplifying -3x(x + 10) + 2x = 30 Reorder the terms: -3x(10 + x) + 2x = 30 (10 * -3x + x * -3x) + 2x = 30 (-30x + -3x2) + 2x = 30 Reorder the terms: -30x + 2x + -3x2 = 30 Combine like terms: -30x + 2x = -28x -28x + -3x2 = 30 Solving -28x + -3x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -28x + -3x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -28x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(30 + 28x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(30 + 28x + 3x2)' equal to zero and attempt to solve: Simplifying 30 + 28x + 3x2 = 0 Solving 30 + 28x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + 9.333333333x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 9.333333333x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 9.333333333x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 9.333333333x + x2 = 0 + -10 9.333333333x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 9.333333333x + x2 = -10 The x term is 9.333333333x. Take half its coefficient (4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. 9.333333333x + 21.77777778 + x2 = -10 + 21.77777778 Reorder the terms: 21.77777778 + 9.333333333x + x2 = -10 + 21.77777778 Combine like terms: -10 + 21.77777778 = 11.77777778 21.77777778 + 9.333333333x + x2 = 11.77777778 Factor a perfect square on the left side: (x + 4.666666667)(x + 4.666666667) = 11.77777778 Calculate the square root of the right side: 3.431876714 Break this problem into two subproblems by setting (x + 4.666666667) equal to 3.431876714 and -3.431876714.Subproblem 1
x + 4.666666667 = 3.431876714 Simplifying x + 4.666666667 = 3.431876714 Reorder the terms: 4.666666667 + x = 3.431876714 Solving 4.666666667 + x = 3.431876714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = 3.431876714 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = 3.431876714 + -4.666666667 x = 3.431876714 + -4.666666667 Combine like terms: 3.431876714 + -4.666666667 = -1.234789953 x = -1.234789953 Simplifying x = -1.234789953Subproblem 2
x + 4.666666667 = -3.431876714 Simplifying x + 4.666666667 = -3.431876714 Reorder the terms: 4.666666667 + x = -3.431876714 Solving 4.666666667 + x = -3.431876714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = -3.431876714 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = -3.431876714 + -4.666666667 x = -3.431876714 + -4.666666667 Combine like terms: -3.431876714 + -4.666666667 = -8.098543381 x = -8.098543381 Simplifying x = -8.098543381Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.234789953, -8.098543381}Solution
x = {-1.234789953, -8.098543381}
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