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Simplifying 4x2 + -8x + -58 = -9 Reorder the terms: -58 + -8x + 4x2 = -9 Solving -58 + -8x + 4x2 = -9 Solving for variable 'x'. Reorder the terms: -58 + 9 + -8x + 4x2 = -9 + 9 Combine like terms: -58 + 9 = -49 -49 + -8x + 4x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -49 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + -2x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -2x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -2x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -2x + x2 = 0 + 12.25 -2x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -2x + x2 = 12.25 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 = 12.25 + 1 Reorder the terms: 1 + -2x + x2 = 12.25 + 1 Combine like terms: 12.25 + 1 = 13.25 1 + -2x + x2 = 13.25 Factor a perfect square on the left side: (x + -1)(x + -1) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -1) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -1 = 3.640054945 Simplifying x + -1 = 3.640054945 Reorder the terms: -1 + x = 3.640054945 Solving -1 + x = 3.640054945 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 = 3.640054945 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.640054945 + 1 x = 3.640054945 + 1 Combine like terms: 3.640054945 + 1 = 4.640054945 x = 4.640054945 Simplifying x = 4.640054945Subproblem 2
x + -1 = -3.640054945 Simplifying x + -1 = -3.640054945 Reorder the terms: -1 + x = -3.640054945 Solving -1 + x = -3.640054945 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 = -3.640054945 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.640054945 + 1 x = -3.640054945 + 1 Combine like terms: -3.640054945 + 1 = -2.640054945 x = -2.640054945 Simplifying x = -2.640054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.640054945, -2.640054945}
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