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Simplifying 20x2 + 10x = 94 Reorder the terms: 10x + 20x2 = 94 Solving 10x + 20x2 = 94 Solving for variable 'x'. Reorder the terms: -94 + 10x + 20x2 = 94 + -94 Combine like terms: 94 + -94 = 0 -94 + 10x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 5x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 5x + 10x2)' equal to zero and attempt to solve: Simplifying -47 + 5x + 10x2 = 0 Solving -47 + 5x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -4.7 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '4.7' to each side of the equation. -4.7 + 0.5x + 4.7 + x2 = 0.0 + 4.7 Reorder the terms: -4.7 + 4.7 + 0.5x + x2 = 0.0 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + 0.5x + x2 = 0.0 + 4.7 0.5x + x2 = 0.0 + 4.7 Combine like terms: 0.0 + 4.7 = 4.7 0.5x + x2 = 4.7 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 4.7 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 4.7 + 0.0625 Combine like terms: 4.7 + 0.0625 = 4.7625 0.0625 + 0.5x + x2 = 4.7625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 4.7625 Calculate the square root of the right side: 2.182315284 Break this problem into two subproblems by setting (x + 0.25) equal to 2.182315284 and -2.182315284.Subproblem 1
x + 0.25 = 2.182315284 Simplifying x + 0.25 = 2.182315284 Reorder the terms: 0.25 + x = 2.182315284 Solving 0.25 + x = 2.182315284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.182315284 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.182315284 + -0.25 x = 2.182315284 + -0.25 Combine like terms: 2.182315284 + -0.25 = 1.932315284 x = 1.932315284 Simplifying x = 1.932315284Subproblem 2
x + 0.25 = -2.182315284 Simplifying x + 0.25 = -2.182315284 Reorder the terms: 0.25 + x = -2.182315284 Solving 0.25 + x = -2.182315284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.182315284 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.182315284 + -0.25 x = -2.182315284 + -0.25 Combine like terms: -2.182315284 + -0.25 = -2.432315284 x = -2.432315284 Simplifying x = -2.432315284Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.932315284, -2.432315284}Solution
x = {1.932315284, -2.432315284}
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