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Simplifying 4x2 + -36x + 81 = 79 Reorder the terms: 81 + -36x + 4x2 = 79 Solving 81 + -36x + 4x2 = 79 Solving for variable 'x'. Reorder the terms: 81 + -79 + -36x + 4x2 = 79 + -79 Combine like terms: 81 + -79 = 2 2 + -36x + 4x2 = 79 + -79 Combine like terms: 79 + -79 = 0 2 + -36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -18x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -18x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + -18x + 2x2 = 0 Solving 1 + -18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -9x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -9x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -9x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -9x + x2 = 0 + -0.5 -9x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -9x + x2 = -0.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -0.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -0.5 + 20.25 Combine like terms: -0.5 + 20.25 = 19.75 20.25 + -9x + x2 = 19.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + -4.5) equal to 4.444097209 and -4.444097209.Subproblem 1
x + -4.5 = 4.444097209 Simplifying x + -4.5 = 4.444097209 Reorder the terms: -4.5 + x = 4.444097209 Solving -4.5 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.444097209 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.444097209 + 4.5 x = 4.444097209 + 4.5 Combine like terms: 4.444097209 + 4.5 = 8.944097209 x = 8.944097209 Simplifying x = 8.944097209Subproblem 2
x + -4.5 = -4.444097209 Simplifying x + -4.5 = -4.444097209 Reorder the terms: -4.5 + x = -4.444097209 Solving -4.5 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.444097209 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.444097209 + 4.5 x = -4.444097209 + 4.5 Combine like terms: -4.444097209 + 4.5 = 0.055902791 x = 0.055902791 Simplifying x = 0.055902791Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.944097209, 0.055902791}Solution
x = {8.944097209, 0.055902791}
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