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Simplifying (3x + -7)(5x + 2) = 10 Reorder the terms: (-7 + 3x)(5x + 2) = 10 Reorder the terms: (-7 + 3x)(2 + 5x) = 10 Multiply (-7 + 3x) * (2 + 5x) (-7(2 + 5x) + 3x * (2 + 5x)) = 10 ((2 * -7 + 5x * -7) + 3x * (2 + 5x)) = 10 ((-14 + -35x) + 3x * (2 + 5x)) = 10 (-14 + -35x + (2 * 3x + 5x * 3x)) = 10 (-14 + -35x + (6x + 15x2)) = 10 Combine like terms: -35x + 6x = -29x (-14 + -29x + 15x2) = 10 Solving -14 + -29x + 15x2 = 10 Solving for variable 'x'. Reorder the terms: -14 + -10 + -29x + 15x2 = 10 + -10 Combine like terms: -14 + -10 = -24 -24 + -29x + 15x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -24 + -29x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.6 + -1.933333333x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -1.933333333x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -1.933333333x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -1.933333333x + x2 = 0 + 1.6 -1.933333333x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -1.933333333x + x2 = 1.6 The x term is -1.933333333x. Take half its coefficient (-0.9666666665). Square it (0.9344444441) and add it to both sides. Add '0.9344444441' to each side of the equation. -1.933333333x + 0.9344444441 + x2 = 1.6 + 0.9344444441 Reorder the terms: 0.9344444441 + -1.933333333x + x2 = 1.6 + 0.9344444441 Combine like terms: 1.6 + 0.9344444441 = 2.5344444441 0.9344444441 + -1.933333333x + x2 = 2.5344444441 Factor a perfect square on the left side: (x + -0.9666666665)(x + -0.9666666665) = 2.5344444441 Calculate the square root of the right side: 1.591993858 Break this problem into two subproblems by setting (x + -0.9666666665) equal to 1.591993858 and -1.591993858.Subproblem 1
x + -0.9666666665 = 1.591993858 Simplifying x + -0.9666666665 = 1.591993858 Reorder the terms: -0.9666666665 + x = 1.591993858 Solving -0.9666666665 + x = 1.591993858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9666666665' to each side of the equation. -0.9666666665 + 0.9666666665 + x = 1.591993858 + 0.9666666665 Combine like terms: -0.9666666665 + 0.9666666665 = 0.0000000000 0.0000000000 + x = 1.591993858 + 0.9666666665 x = 1.591993858 + 0.9666666665 Combine like terms: 1.591993858 + 0.9666666665 = 2.5586605245 x = 2.5586605245 Simplifying x = 2.5586605245Subproblem 2
x + -0.9666666665 = -1.591993858 Simplifying x + -0.9666666665 = -1.591993858 Reorder the terms: -0.9666666665 + x = -1.591993858 Solving -0.9666666665 + x = -1.591993858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9666666665' to each side of the equation. -0.9666666665 + 0.9666666665 + x = -1.591993858 + 0.9666666665 Combine like terms: -0.9666666665 + 0.9666666665 = 0.0000000000 0.0000000000 + x = -1.591993858 + 0.9666666665 x = -1.591993858 + 0.9666666665 Combine like terms: -1.591993858 + 0.9666666665 = -0.6253271915 x = -0.6253271915 Simplifying x = -0.6253271915Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5586605245, -0.6253271915}
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