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Simplifying 4x2 + 8x + -9 = 85 Reorder the terms: -9 + 8x + 4x2 = 85 Solving -9 + 8x + 4x2 = 85 Solving for variable 'x'. Reorder the terms: -9 + -85 + 8x + 4x2 = 85 + -85 Combine like terms: -9 + -85 = -94 -94 + 8x + 4x2 = 85 + -85 Combine like terms: 85 + -85 = 0 -94 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -47 + 4x + 2x2 = 0 Solving -47 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23.5 + 2x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + 2x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + 2x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + 2x + x2 = 0 + 23.5 2x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 2x + x2 = 23.5 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 = 23.5 + 1 Reorder the terms: 1 + 2x + x2 = 23.5 + 1 Combine like terms: 23.5 + 1 = 24.5 1 + 2x + x2 = 24.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 24.5 Calculate the square root of the right side: 4.949747468 Break this problem into two subproblems by setting (x + 1) equal to 4.949747468 and -4.949747468.Subproblem 1
x + 1 = 4.949747468 Simplifying x + 1 = 4.949747468 Reorder the terms: 1 + x = 4.949747468 Solving 1 + x = 4.949747468 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 = 4.949747468 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.949747468 + -1 x = 4.949747468 + -1 Combine like terms: 4.949747468 + -1 = 3.949747468 x = 3.949747468 Simplifying x = 3.949747468Subproblem 2
x + 1 = -4.949747468 Simplifying x + 1 = -4.949747468 Reorder the terms: 1 + x = -4.949747468 Solving 1 + x = -4.949747468 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 = -4.949747468 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.949747468 + -1 x = -4.949747468 + -1 Combine like terms: -4.949747468 + -1 = -5.949747468 x = -5.949747468 Simplifying x = -5.949747468Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.949747468, -5.949747468}Solution
x = {3.949747468, -5.949747468}
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