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Simplifying -17x2 + -23x + 4 = 0 Reorder the terms: 4 + -23x + -17x2 = 0 Solving 4 + -23x + -17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -0.2352941176 + 1.352941176x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + 1.352941176x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + 1.352941176x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + 1.352941176x + x2 = 0 + 0.2352941176 1.352941176x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 1.352941176x + x2 = 0.2352941176 The x term is 1.352941176x. Take half its coefficient (0.676470588). Square it (0.4576124564) and add it to both sides. Add '0.4576124564' to each side of the equation. 1.352941176x + 0.4576124564 + x2 = 0.2352941176 + 0.4576124564 Reorder the terms: 0.4576124564 + 1.352941176x + x2 = 0.2352941176 + 0.4576124564 Combine like terms: 0.2352941176 + 0.4576124564 = 0.692906574 0.4576124564 + 1.352941176x + x2 = 0.692906574 Factor a perfect square on the left side: (x + 0.676470588)(x + 0.676470588) = 0.692906574 Calculate the square root of the right side: 0.8324101 Break this problem into two subproblems by setting (x + 0.676470588) equal to 0.8324101 and -0.8324101.Subproblem 1
x + 0.676470588 = 0.8324101 Simplifying x + 0.676470588 = 0.8324101 Reorder the terms: 0.676470588 + x = 0.8324101 Solving 0.676470588 + x = 0.8324101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.676470588' to each side of the equation. 0.676470588 + -0.676470588 + x = 0.8324101 + -0.676470588 Combine like terms: 0.676470588 + -0.676470588 = 0.000000000 0.000000000 + x = 0.8324101 + -0.676470588 x = 0.8324101 + -0.676470588 Combine like terms: 0.8324101 + -0.676470588 = 0.155939512 x = 0.155939512 Simplifying x = 0.155939512Subproblem 2
x + 0.676470588 = -0.8324101 Simplifying x + 0.676470588 = -0.8324101 Reorder the terms: 0.676470588 + x = -0.8324101 Solving 0.676470588 + x = -0.8324101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.676470588' to each side of the equation. 0.676470588 + -0.676470588 + x = -0.8324101 + -0.676470588 Combine like terms: 0.676470588 + -0.676470588 = 0.000000000 0.000000000 + x = -0.8324101 + -0.676470588 x = -0.8324101 + -0.676470588 Combine like terms: -0.8324101 + -0.676470588 = -1.508880688 x = -1.508880688 Simplifying x = -1.508880688Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.155939512, -1.508880688}
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