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Simplifying 10x2 + 4x = 500 Reorder the terms: 4x + 10x2 = 500 Solving 4x + 10x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 4x + 10x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 4x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-250 + 2x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-250 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying -250 + 2x + 5x2 = 0 Solving -250 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -50 + 0.4x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 0.4x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 0.4x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 0.4x + x2 = 0 + 50 0.4x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 0.4x + x2 = 50 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 50 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 50 + 0.04 Combine like terms: 50 + 0.04 = 50.04 0.04 + 0.4x + x2 = 50.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 50.04 Calculate the square root of the right side: 7.073895674 Break this problem into two subproblems by setting (x + 0.2) equal to 7.073895674 and -7.073895674.Subproblem 1
x + 0.2 = 7.073895674 Simplifying x + 0.2 = 7.073895674 Reorder the terms: 0.2 + x = 7.073895674 Solving 0.2 + x = 7.073895674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 7.073895674 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 7.073895674 + -0.2 x = 7.073895674 + -0.2 Combine like terms: 7.073895674 + -0.2 = 6.873895674 x = 6.873895674 Simplifying x = 6.873895674Subproblem 2
x + 0.2 = -7.073895674 Simplifying x + 0.2 = -7.073895674 Reorder the terms: 0.2 + x = -7.073895674 Solving 0.2 + x = -7.073895674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -7.073895674 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -7.073895674 + -0.2 x = -7.073895674 + -0.2 Combine like terms: -7.073895674 + -0.2 = -7.273895674 x = -7.273895674 Simplifying x = -7.273895674Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.873895674, -7.273895674}Solution
x = {6.873895674, -7.273895674}
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