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Simplifying 0 = 84 + 18X + -2X2 Solving 0 = 84 + 18X + -2X2 Solving for variable 'X'. Combine like terms: 0 + -84 = -84 -84 + -18X + 2X2 = 84 + 18X + -2X2 + -84 + -18X + 2X2 Reorder the terms: -84 + -18X + 2X2 = 84 + -84 + 18X + -18X + -2X2 + 2X2 Combine like terms: 84 + -84 = 0 -84 + -18X + 2X2 = 0 + 18X + -18X + -2X2 + 2X2 -84 + -18X + 2X2 = 18X + -18X + -2X2 + 2X2 Combine like terms: 18X + -18X = 0 -84 + -18X + 2X2 = 0 + -2X2 + 2X2 -84 + -18X + 2X2 = -2X2 + 2X2 Combine like terms: -2X2 + 2X2 = 0 -84 + -18X + 2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + -9X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + -9X + X2)' equal to zero and attempt to solve: Simplifying -42 + -9X + X2 = 0 Solving -42 + -9X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -9X + 42 + X2 = 0 + 42 Reorder the terms: -42 + 42 + -9X + X2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -9X + X2 = 0 + 42 -9X + X2 = 0 + 42 Combine like terms: 0 + 42 = 42 -9X + X2 = 42 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 = 42 + 20.25 Reorder the terms: 20.25 + -9X + X2 = 42 + 20.25 Combine like terms: 42 + 20.25 = 62.25 20.25 + -9X + X2 = 62.25 Factor a perfect square on the left side: (X + -4.5)(X + -4.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (X + -4.5) equal to 7.889866919 and -7.889866919.Subproblem 1
X + -4.5 = 7.889866919 Simplifying X + -4.5 = 7.889866919 Reorder the terms: -4.5 + X = 7.889866919 Solving -4.5 + X = 7.889866919 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 = 7.889866919 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X = 7.889866919 + 4.5 X = 7.889866919 + 4.5 Combine like terms: 7.889866919 + 4.5 = 12.389866919 X = 12.389866919 Simplifying X = 12.389866919Subproblem 2
X + -4.5 = -7.889866919 Simplifying X + -4.5 = -7.889866919 Reorder the terms: -4.5 + X = -7.889866919 Solving -4.5 + X = -7.889866919 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 = -7.889866919 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X = -7.889866919 + 4.5 X = -7.889866919 + 4.5 Combine like terms: -7.889866919 + 4.5 = -3.389866919 X = -3.389866919 Simplifying X = -3.389866919Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.389866919, -3.389866919}Solution
X = {12.389866919, -3.389866919}
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