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Simplifying -12x2 + 11x + -5x2 + 4 = 0 Reorder the terms: 4 + 11x + -12x2 + -5x2 = 0 Combine like terms: -12x2 + -5x2 = -17x2 4 + 11x + -17x2 = 0 Solving 4 + 11x + -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 + -0.6470588235x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + -0.6470588235x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + -0.6470588235x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + -0.6470588235x + x2 = 0 + 0.2352941176 -0.6470588235x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 -0.6470588235x + x2 = 0.2352941176 The x term is -0.6470588235x. Take half its coefficient (-0.3235294118). Square it (0.1046712803) and add it to both sides. Add '0.1046712803' to each side of the equation. -0.6470588235x + 0.1046712803 + x2 = 0.2352941176 + 0.1046712803 Reorder the terms: 0.1046712803 + -0.6470588235x + x2 = 0.2352941176 + 0.1046712803 Combine like terms: 0.2352941176 + 0.1046712803 = 0.3399653979 0.1046712803 + -0.6470588235x + x2 = 0.3399653979 Factor a perfect square on the left side: (x + -0.3235294118)(x + -0.3235294118) = 0.3399653979 Calculate the square root of the right side: 0.583065518 Break this problem into two subproblems by setting (x + -0.3235294118) equal to 0.583065518 and -0.583065518.Subproblem 1
x + -0.3235294118 = 0.583065518 Simplifying x + -0.3235294118 = 0.583065518 Reorder the terms: -0.3235294118 + x = 0.583065518 Solving -0.3235294118 + x = 0.583065518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3235294118' to each side of the equation. -0.3235294118 + 0.3235294118 + x = 0.583065518 + 0.3235294118 Combine like terms: -0.3235294118 + 0.3235294118 = 0.0000000000 0.0000000000 + x = 0.583065518 + 0.3235294118 x = 0.583065518 + 0.3235294118 Combine like terms: 0.583065518 + 0.3235294118 = 0.9065949298 x = 0.9065949298 Simplifying x = 0.9065949298Subproblem 2
x + -0.3235294118 = -0.583065518 Simplifying x + -0.3235294118 = -0.583065518 Reorder the terms: -0.3235294118 + x = -0.583065518 Solving -0.3235294118 + x = -0.583065518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3235294118' to each side of the equation. -0.3235294118 + 0.3235294118 + x = -0.583065518 + 0.3235294118 Combine like terms: -0.3235294118 + 0.3235294118 = 0.0000000000 0.0000000000 + x = -0.583065518 + 0.3235294118 x = -0.583065518 + 0.3235294118 Combine like terms: -0.583065518 + 0.3235294118 = -0.2595361062 x = -0.2595361062 Simplifying x = -0.2595361062Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9065949298, -0.2595361062}
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