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Simplifying 17x2 + -10x + -12 = 0 Reorder the terms: -12 + -10x + 17x2 = 0 Solving -12 + -10x + 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'. -0.7058823529 + -0.5882352941x + x2 = 0 Move the constant term to the right: Add '0.7058823529' to each side of the equation. -0.7058823529 + -0.5882352941x + 0.7058823529 + x2 = 0 + 0.7058823529 Reorder the terms: -0.7058823529 + 0.7058823529 + -0.5882352941x + x2 = 0 + 0.7058823529 Combine like terms: -0.7058823529 + 0.7058823529 = 0.0000000000 0.0000000000 + -0.5882352941x + x2 = 0 + 0.7058823529 -0.5882352941x + x2 = 0 + 0.7058823529 Combine like terms: 0 + 0.7058823529 = 0.7058823529 -0.5882352941x + x2 = 0.7058823529 The x term is -0.5882352941x. Take half its coefficient (-0.2941176471). Square it (0.08650519034) and add it to both sides. Add '0.08650519034' to each side of the equation. -0.5882352941x + 0.08650519034 + x2 = 0.7058823529 + 0.08650519034 Reorder the terms: 0.08650519034 + -0.5882352941x + x2 = 0.7058823529 + 0.08650519034 Combine like terms: 0.7058823529 + 0.08650519034 = 0.79238754324 0.08650519034 + -0.5882352941x + x2 = 0.79238754324 Factor a perfect square on the left side: (x + -0.2941176471)(x + -0.2941176471) = 0.79238754324 Calculate the square root of the right side: 0.890161526 Break this problem into two subproblems by setting (x + -0.2941176471) equal to 0.890161526 and -0.890161526.Subproblem 1
x + -0.2941176471 = 0.890161526 Simplifying x + -0.2941176471 = 0.890161526 Reorder the terms: -0.2941176471 + x = 0.890161526 Solving -0.2941176471 + x = 0.890161526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2941176471' to each side of the equation. -0.2941176471 + 0.2941176471 + x = 0.890161526 + 0.2941176471 Combine like terms: -0.2941176471 + 0.2941176471 = 0.0000000000 0.0000000000 + x = 0.890161526 + 0.2941176471 x = 0.890161526 + 0.2941176471 Combine like terms: 0.890161526 + 0.2941176471 = 1.1842791731 x = 1.1842791731 Simplifying x = 1.1842791731Subproblem 2
x + -0.2941176471 = -0.890161526 Simplifying x + -0.2941176471 = -0.890161526 Reorder the terms: -0.2941176471 + x = -0.890161526 Solving -0.2941176471 + x = -0.890161526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2941176471' to each side of the equation. -0.2941176471 + 0.2941176471 + x = -0.890161526 + 0.2941176471 Combine like terms: -0.2941176471 + 0.2941176471 = 0.0000000000 0.0000000000 + x = -0.890161526 + 0.2941176471 x = -0.890161526 + 0.2941176471 Combine like terms: -0.890161526 + 0.2941176471 = -0.5960438789 x = -0.5960438789 Simplifying x = -0.5960438789Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1842791731, -0.5960438789}
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