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Simplifying 17x2 + -42x + -8 = 0 Reorder the terms: -8 + -42x + 17x2 = 0 Solving -8 + -42x + 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'. -0.4705882353 + -2.470588235x + x2 = 0 Move the constant term to the right: Add '0.4705882353' to each side of the equation. -0.4705882353 + -2.470588235x + 0.4705882353 + x2 = 0 + 0.4705882353 Reorder the terms: -0.4705882353 + 0.4705882353 + -2.470588235x + x2 = 0 + 0.4705882353 Combine like terms: -0.4705882353 + 0.4705882353 = 0.0000000000 0.0000000000 + -2.470588235x + x2 = 0 + 0.4705882353 -2.470588235x + x2 = 0 + 0.4705882353 Combine like terms: 0 + 0.4705882353 = 0.4705882353 -2.470588235x + x2 = 0.4705882353 The x term is -2.470588235x. Take half its coefficient (-1.235294118). Square it (1.525951558) and add it to both sides. Add '1.525951558' to each side of the equation. -2.470588235x + 1.525951558 + x2 = 0.4705882353 + 1.525951558 Reorder the terms: 1.525951558 + -2.470588235x + x2 = 0.4705882353 + 1.525951558 Combine like terms: 0.4705882353 + 1.525951558 = 1.9965397933 1.525951558 + -2.470588235x + x2 = 1.9965397933 Factor a perfect square on the left side: (x + -1.235294118)(x + -1.235294118) = 1.9965397933 Calculate the square root of the right side: 1.412989665 Break this problem into two subproblems by setting (x + -1.235294118) equal to 1.412989665 and -1.412989665.Subproblem 1
x + -1.235294118 = 1.412989665 Simplifying x + -1.235294118 = 1.412989665 Reorder the terms: -1.235294118 + x = 1.412989665 Solving -1.235294118 + x = 1.412989665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.235294118' to each side of the equation. -1.235294118 + 1.235294118 + x = 1.412989665 + 1.235294118 Combine like terms: -1.235294118 + 1.235294118 = 0.000000000 0.000000000 + x = 1.412989665 + 1.235294118 x = 1.412989665 + 1.235294118 Combine like terms: 1.412989665 + 1.235294118 = 2.648283783 x = 2.648283783 Simplifying x = 2.648283783Subproblem 2
x + -1.235294118 = -1.412989665 Simplifying x + -1.235294118 = -1.412989665 Reorder the terms: -1.235294118 + x = -1.412989665 Solving -1.235294118 + x = -1.412989665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.235294118' to each side of the equation. -1.235294118 + 1.235294118 + x = -1.412989665 + 1.235294118 Combine like terms: -1.235294118 + 1.235294118 = 0.000000000 0.000000000 + x = -1.412989665 + 1.235294118 x = -1.412989665 + 1.235294118 Combine like terms: -1.412989665 + 1.235294118 = -0.177695547 x = -0.177695547 Simplifying x = -0.177695547Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.648283783, -0.177695547}
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