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Simplifying 10x2 + 20x + -94 = 0 Reorder the terms: -94 + 20x + 10x2 = 0 Solving -94 + 20x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 10x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 10x + 5x2)' equal to zero and attempt to solve: Simplifying -47 + 10x + 5x2 = 0 Solving -47 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.4 + 2x + x2 = 0 Move the constant term to the right: Add '9.4' to each side of the equation. -9.4 + 2x + 9.4 + x2 = 0 + 9.4 Reorder the terms: -9.4 + 9.4 + 2x + x2 = 0 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + 2x + x2 = 0 + 9.4 2x + x2 = 0 + 9.4 Combine like terms: 0 + 9.4 = 9.4 2x + x2 = 9.4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 9.4 + 1 Reorder the terms: 1 + 2x + x2 = 9.4 + 1 Combine like terms: 9.4 + 1 = 10.4 1 + 2x + x2 = 10.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 10.4 Calculate the square root of the right side: 3.224903099 Break this problem into two subproblems by setting (x + 1) equal to 3.224903099 and -3.224903099.Subproblem 1
x + 1 = 3.224903099 Simplifying x + 1 = 3.224903099 Reorder the terms: 1 + x = 3.224903099 Solving 1 + x = 3.224903099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.224903099 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.224903099 + -1 x = 3.224903099 + -1 Combine like terms: 3.224903099 + -1 = 2.224903099 x = 2.224903099 Simplifying x = 2.224903099Subproblem 2
x + 1 = -3.224903099 Simplifying x + 1 = -3.224903099 Reorder the terms: 1 + x = -3.224903099 Solving 1 + x = -3.224903099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.224903099 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.224903099 + -1 x = -3.224903099 + -1 Combine like terms: -3.224903099 + -1 = -4.224903099 x = -4.224903099 Simplifying x = -4.224903099Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.224903099, -4.224903099}Solution
x = {2.224903099, -4.224903099}
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