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Simplifying 190 = 2x2 + 4x Reorder the terms: 190 = 4x + 2x2 Solving 190 = 4x + 2x2 Solving for variable 'x'. Reorder the terms: 190 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 190 + -4x + -2x2 = 0 + 2x2 + -2x2 190 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 190 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(95 + -2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(95 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 95 + -2x + -1x2 = 0 Solving 95 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -95 + 2x + x2 = 0 Move the constant term to the right: Add '95' to each side of the equation. -95 + 2x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + 2x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 2x + x2 = 0 + 95 2x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 2x + x2 = 95 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 = 95 + 1 Reorder the terms: 1 + 2x + x2 = 95 + 1 Combine like terms: 95 + 1 = 96 1 + 2x + x2 = 96 Factor a perfect square on the left side: (x + 1)(x + 1) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 1) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 1 = 9.797958971 Simplifying x + 1 = 9.797958971 Reorder the terms: 1 + x = 9.797958971 Solving 1 + x = 9.797958971 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 = 9.797958971 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.797958971 + -1 x = 9.797958971 + -1 Combine like terms: 9.797958971 + -1 = 8.797958971 x = 8.797958971 Simplifying x = 8.797958971Subproblem 2
x + 1 = -9.797958971 Simplifying x + 1 = -9.797958971 Reorder the terms: 1 + x = -9.797958971 Solving 1 + x = -9.797958971 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 = -9.797958971 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.797958971 + -1 x = -9.797958971 + -1 Combine like terms: -9.797958971 + -1 = -10.797958971 x = -10.797958971 Simplifying x = -10.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.797958971, -10.797958971}Solution
x = {8.797958971, -10.797958971}
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