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Simplifying 2(7 + -1x) * 4x = 20 Reorder the terms for easier multiplication: 2 * 4x(7 + -1x) = 20 Multiply 2 * 4 8x(7 + -1x) = 20 (7 * 8x + -1x * 8x) = 20 (56x + -8x2) = 20 Solving 56x + -8x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 56x + -8x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 56x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 14x + -2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 14x + -2x2)' equal to zero and attempt to solve: Simplifying -5 + 14x + -2x2 = 0 Solving -5 + 14x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -7x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -7x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -7x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -7x + x2 = 0 + -2.5 -7x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -7x + x2 = -2.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -2.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -2.5 + 12.25 Combine like terms: -2.5 + 12.25 = 9.75 12.25 + -7x + x2 = 9.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + -3.5) equal to 3.122498999 and -3.122498999.Subproblem 1
x + -3.5 = 3.122498999 Simplifying x + -3.5 = 3.122498999 Reorder the terms: -3.5 + x = 3.122498999 Solving -3.5 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.122498999 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.122498999 + 3.5 x = 3.122498999 + 3.5 Combine like terms: 3.122498999 + 3.5 = 6.622498999 x = 6.622498999 Simplifying x = 6.622498999Subproblem 2
x + -3.5 = -3.122498999 Simplifying x + -3.5 = -3.122498999 Reorder the terms: -3.5 + x = -3.122498999 Solving -3.5 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.122498999 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.122498999 + 3.5 x = -3.122498999 + 3.5 Combine like terms: -3.122498999 + 3.5 = 0.377501001 x = 0.377501001 Simplifying x = 0.377501001Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.622498999, 0.377501001}Solution
x = {6.622498999, 0.377501001}
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