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Simplifying 8x2 + 18x = 4 Reorder the terms: 18x + 8x2 = 4 Solving 18x + 8x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 18x + 8x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 18x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 9x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying -2 + 9x + 4x2 = 0 Solving -2 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + 2.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2.25x + x2 = 0 + 0.5 2.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2.25x + x2 = 0.5 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 0.5 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 0.5 + 1.265625 Combine like terms: 0.5 + 1.265625 = 1.765625 1.265625 + 2.25x + x2 = 1.765625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + 1.125) equal to 1.328768227 and -1.328768227.Subproblem 1
x + 1.125 = 1.328768227 Simplifying x + 1.125 = 1.328768227 Reorder the terms: 1.125 + x = 1.328768227 Solving 1.125 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.328768227 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.328768227 + -1.125 x = 1.328768227 + -1.125 Combine like terms: 1.328768227 + -1.125 = 0.203768227 x = 0.203768227 Simplifying x = 0.203768227Subproblem 2
x + 1.125 = -1.328768227 Simplifying x + 1.125 = -1.328768227 Reorder the terms: 1.125 + x = -1.328768227 Solving 1.125 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.328768227 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.328768227 + -1.125 x = -1.328768227 + -1.125 Combine like terms: -1.328768227 + -1.125 = -2.453768227 x = -2.453768227 Simplifying x = -2.453768227Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.203768227, -2.453768227}Solution
x = {0.203768227, -2.453768227}
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