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Simplifying 10x(2x + -5) + -5 = 20 Reorder the terms: 10x(-5 + 2x) + -5 = 20 (-5 * 10x + 2x * 10x) + -5 = 20 (-50x + 20x2) + -5 = 20 Reorder the terms: -5 + -50x + 20x2 = 20 Solving -5 + -50x + 20x2 = 20 Solving for variable 'x'. Reorder the terms: -5 + -20 + -50x + 20x2 = 20 + -20 Combine like terms: -5 + -20 = -25 -25 + -50x + 20x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -25 + -50x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + -10x + 4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -10x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + -10x + 4x2 = 0 Solving -5 + -10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.5x + x2 = 0 + 1.25 -2.5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.5x + x2 = 1.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.25 + 1.5625 Combine like terms: 1.25 + 1.5625 = 2.8125 1.5625 + -2.5x + x2 = 2.8125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x + -1.25) equal to 1.677050983 and -1.677050983.Subproblem 1
x + -1.25 = 1.677050983 Simplifying x + -1.25 = 1.677050983 Reorder the terms: -1.25 + x = 1.677050983 Solving -1.25 + x = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.677050983 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.677050983 + 1.25 x = 1.677050983 + 1.25 Combine like terms: 1.677050983 + 1.25 = 2.927050983 x = 2.927050983 Simplifying x = 2.927050983Subproblem 2
x + -1.25 = -1.677050983 Simplifying x + -1.25 = -1.677050983 Reorder the terms: -1.25 + x = -1.677050983 Solving -1.25 + x = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.677050983 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.677050983 + 1.25 x = -1.677050983 + 1.25 Combine like terms: -1.677050983 + 1.25 = -0.427050983 x = -0.427050983 Simplifying x = -0.427050983Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.927050983, -0.427050983}Solution
x = {2.927050983, -0.427050983}
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