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Simplifying 12(2x + 2) = 7x(5x + -1) Reorder the terms: 12(2 + 2x) = 7x(5x + -1) (2 * 12 + 2x * 12) = 7x(5x + -1) (24 + 24x) = 7x(5x + -1) Reorder the terms: 24 + 24x = 7x(-1 + 5x) 24 + 24x = (-1 * 7x + 5x * 7x) 24 + 24x = (-7x + 35x2) Solving 24 + 24x = -7x + 35x2 Solving for variable 'x'. Combine like terms: 24x + 7x = 31x 24 + 31x + -35x2 = -7x + 35x2 + 7x + -35x2 Reorder the terms: 24 + 31x + -35x2 = -7x + 7x + 35x2 + -35x2 Combine like terms: -7x + 7x = 0 24 + 31x + -35x2 = 0 + 35x2 + -35x2 24 + 31x + -35x2 = 35x2 + -35x2 Combine like terms: 35x2 + -35x2 = 0 24 + 31x + -35x2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -0.6857142857 + -0.8857142857x + x2 = 0 Move the constant term to the right: Add '0.6857142857' to each side of the equation. -0.6857142857 + -0.8857142857x + 0.6857142857 + x2 = 0 + 0.6857142857 Reorder the terms: -0.6857142857 + 0.6857142857 + -0.8857142857x + x2 = 0 + 0.6857142857 Combine like terms: -0.6857142857 + 0.6857142857 = 0.0000000000 0.0000000000 + -0.8857142857x + x2 = 0 + 0.6857142857 -0.8857142857x + x2 = 0 + 0.6857142857 Combine like terms: 0 + 0.6857142857 = 0.6857142857 -0.8857142857x + x2 = 0.6857142857 The x term is -0.8857142857x. Take half its coefficient (-0.4428571429). Square it (0.1961224490) and add it to both sides. Add '0.1961224490' to each side of the equation. -0.8857142857x + 0.1961224490 + x2 = 0.6857142857 + 0.1961224490 Reorder the terms: 0.1961224490 + -0.8857142857x + x2 = 0.6857142857 + 0.1961224490 Combine like terms: 0.6857142857 + 0.1961224490 = 0.8818367347 0.1961224490 + -0.8857142857x + x2 = 0.8818367347 Factor a perfect square on the left side: (x + -0.4428571429)(x + -0.4428571429) = 0.8818367347 Calculate the square root of the right side: 0.939061625 Break this problem into two subproblems by setting (x + -0.4428571429) equal to 0.939061625 and -0.939061625.Subproblem 1
x + -0.4428571429 = 0.939061625 Simplifying x + -0.4428571429 = 0.939061625 Reorder the terms: -0.4428571429 + x = 0.939061625 Solving -0.4428571429 + x = 0.939061625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4428571429' to each side of the equation. -0.4428571429 + 0.4428571429 + x = 0.939061625 + 0.4428571429 Combine like terms: -0.4428571429 + 0.4428571429 = 0.0000000000 0.0000000000 + x = 0.939061625 + 0.4428571429 x = 0.939061625 + 0.4428571429 Combine like terms: 0.939061625 + 0.4428571429 = 1.3819187679 x = 1.3819187679 Simplifying x = 1.3819187679Subproblem 2
x + -0.4428571429 = -0.939061625 Simplifying x + -0.4428571429 = -0.939061625 Reorder the terms: -0.4428571429 + x = -0.939061625 Solving -0.4428571429 + x = -0.939061625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4428571429' to each side of the equation. -0.4428571429 + 0.4428571429 + x = -0.939061625 + 0.4428571429 Combine like terms: -0.4428571429 + 0.4428571429 = 0.0000000000 0.0000000000 + x = -0.939061625 + 0.4428571429 x = -0.939061625 + 0.4428571429 Combine like terms: -0.939061625 + 0.4428571429 = -0.4962044821 x = -0.4962044821 Simplifying x = -0.4962044821Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3819187679, -0.4962044821}
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