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Simplifying (2x + -9) * 3(5x + 7) = 11 Reorder the terms: (-9 + 2x) * 3(5x + 7) = 11 Reorder the terms: (-9 + 2x) * 3(7 + 5x) = 11 Reorder the terms for easier multiplication: 3(-9 + 2x)(7 + 5x) = 11 Multiply (-9 + 2x) * (7 + 5x) 3(-9(7 + 5x) + 2x * (7 + 5x)) = 11 3((7 * -9 + 5x * -9) + 2x * (7 + 5x)) = 11 3((-63 + -45x) + 2x * (7 + 5x)) = 11 3(-63 + -45x + (7 * 2x + 5x * 2x)) = 11 3(-63 + -45x + (14x + 10x2)) = 11 Combine like terms: -45x + 14x = -31x 3(-63 + -31x + 10x2) = 11 (-63 * 3 + -31x * 3 + 10x2 * 3) = 11 (-189 + -93x + 30x2) = 11 Solving -189 + -93x + 30x2 = 11 Solving for variable 'x'. Reorder the terms: -189 + -11 + -93x + 30x2 = 11 + -11 Combine like terms: -189 + -11 = -200 -200 + -93x + 30x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -200 + -93x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -6.666666667 + -3.1x + x2 = 0.0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -3.1x + 6.666666667 + x2 = 0.0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -3.1x + x2 = 0.0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -3.1x + x2 = 0.0 + 6.666666667 -3.1x + x2 = 0.0 + 6.666666667 Combine like terms: 0.0 + 6.666666667 = 6.666666667 -3.1x + x2 = 6.666666667 The x term is -3.1x. Take half its coefficient (-1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. -3.1x + 2.4025 + x2 = 6.666666667 + 2.4025 Reorder the terms: 2.4025 + -3.1x + x2 = 6.666666667 + 2.4025 Combine like terms: 6.666666667 + 2.4025 = 9.069166667 2.4025 + -3.1x + x2 = 9.069166667 Factor a perfect square on the left side: (x + -1.55)(x + -1.55) = 9.069166667 Calculate the square root of the right side: 3.011505714 Break this problem into two subproblems by setting (x + -1.55) equal to 3.011505714 and -3.011505714.Subproblem 1
x + -1.55 = 3.011505714 Simplifying x + -1.55 = 3.011505714 Reorder the terms: -1.55 + x = 3.011505714 Solving -1.55 + x = 3.011505714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = 3.011505714 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = 3.011505714 + 1.55 x = 3.011505714 + 1.55 Combine like terms: 3.011505714 + 1.55 = 4.561505714 x = 4.561505714 Simplifying x = 4.561505714Subproblem 2
x + -1.55 = -3.011505714 Simplifying x + -1.55 = -3.011505714 Reorder the terms: -1.55 + x = -3.011505714 Solving -1.55 + x = -3.011505714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = -3.011505714 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = -3.011505714 + 1.55 x = -3.011505714 + 1.55 Combine like terms: -3.011505714 + 1.55 = -1.461505714 x = -1.461505714 Simplifying x = -1.461505714Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.561505714, -1.461505714}
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