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Simplifying (5x + -7)(4x) * 70 = 180 Reorder the terms: (-7 + 5x)(4x) * 70 = 180 Remove parenthesis around (4x) (-7 + 5x) * 4x * 70 = 180 Reorder the terms for easier multiplication: 4 * 70x(-7 + 5x) = 180 Multiply 4 * 70 280x(-7 + 5x) = 180 (-7 * 280x + 5x * 280x) = 180 (-1960x + 1400x2) = 180 Solving -1960x + 1400x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -1960x + 1400x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -1960x + 1400x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-9 + -98x + 70x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-9 + -98x + 70x2)' equal to zero and attempt to solve: Simplifying -9 + -98x + 70x2 = 0 Solving -9 + -98x + 70x2 = 0 Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. -0.1285714286 + -1.4x + x2 = 0.0 Move the constant term to the right: Add '0.1285714286' to each side of the equation. -0.1285714286 + -1.4x + 0.1285714286 + x2 = 0.0 + 0.1285714286 Reorder the terms: -0.1285714286 + 0.1285714286 + -1.4x + x2 = 0.0 + 0.1285714286 Combine like terms: -0.1285714286 + 0.1285714286 = 0.0000000000 0.0000000000 + -1.4x + x2 = 0.0 + 0.1285714286 -1.4x + x2 = 0.0 + 0.1285714286 Combine like terms: 0.0 + 0.1285714286 = 0.1285714286 -1.4x + x2 = 0.1285714286 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.1285714286 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.1285714286 + 0.49 Combine like terms: 0.1285714286 + 0.49 = 0.6185714286 0.49 + -1.4x + x2 = 0.6185714286 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.6185714286 Calculate the square root of the right side: 0.786493121 Break this problem into two subproblems by setting (x + -0.7) equal to 0.786493121 and -0.786493121.Subproblem 1
x + -0.7 = 0.786493121 Simplifying x + -0.7 = 0.786493121 Reorder the terms: -0.7 + x = 0.786493121 Solving -0.7 + x = 0.786493121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.786493121 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.786493121 + 0.7 x = 0.786493121 + 0.7 Combine like terms: 0.786493121 + 0.7 = 1.486493121 x = 1.486493121 Simplifying x = 1.486493121Subproblem 2
x + -0.7 = -0.786493121 Simplifying x + -0.7 = -0.786493121 Reorder the terms: -0.7 + x = -0.786493121 Solving -0.7 + x = -0.786493121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.786493121 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.786493121 + 0.7 x = -0.786493121 + 0.7 Combine like terms: -0.786493121 + 0.7 = -0.086493121 x = -0.086493121 Simplifying x = -0.086493121Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.486493121, -0.086493121}Solution
x = {1.486493121, -0.086493121}
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