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Simplifying 4x2 + 12x + 20 = 90 Reorder the terms: 20 + 12x + 4x2 = 90 Solving 20 + 12x + 4x2 = 90 Solving for variable 'x'. Reorder the terms: 20 + -90 + 12x + 4x2 = 90 + -90 Combine like terms: 20 + -90 = -70 -70 + 12x + 4x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -70 + 12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 6x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying -35 + 6x + 2x2 = 0 Solving -35 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + 3x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 3x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 3x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 3x + x2 = 0 + 17.5 3x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 3x + x2 = 17.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 17.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 17.5 + 2.25 Combine like terms: 17.5 + 2.25 = 19.75 2.25 + 3x + x2 = 19.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + 1.5) equal to 4.444097209 and -4.444097209.Subproblem 1
x + 1.5 = 4.444097209 Simplifying x + 1.5 = 4.444097209 Reorder the terms: 1.5 + x = 4.444097209 Solving 1.5 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.444097209 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.444097209 + -1.5 x = 4.444097209 + -1.5 Combine like terms: 4.444097209 + -1.5 = 2.944097209 x = 2.944097209 Simplifying x = 2.944097209Subproblem 2
x + 1.5 = -4.444097209 Simplifying x + 1.5 = -4.444097209 Reorder the terms: 1.5 + x = -4.444097209 Solving 1.5 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.444097209 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.444097209 + -1.5 x = -4.444097209 + -1.5 Combine like terms: -4.444097209 + -1.5 = -5.944097209 x = -5.944097209 Simplifying x = -5.944097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.944097209, -5.944097209}Solution
x = {2.944097209, -5.944097209}
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