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Simplifying -10x2 + -6x + -7x2 + 8 + 13x = 0 Reorder the terms: 8 + -6x + 13x + -10x2 + -7x2 = 0 Combine like terms: -6x + 13x = 7x 8 + 7x + -10x2 + -7x2 = 0 Combine like terms: -10x2 + -7x2 = -17x2 8 + 7x + -17x2 = 0 Solving 8 + 7x + -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 + -0.4117647059x + x2 = 0 Move the constant term to the right: Add '0.4705882353' to each side of the equation. -0.4705882353 + -0.4117647059x + 0.4705882353 + x2 = 0 + 0.4705882353 Reorder the terms: -0.4705882353 + 0.4705882353 + -0.4117647059x + x2 = 0 + 0.4705882353 Combine like terms: -0.4705882353 + 0.4705882353 = 0.0000000000 0.0000000000 + -0.4117647059x + x2 = 0 + 0.4705882353 -0.4117647059x + x2 = 0 + 0.4705882353 Combine like terms: 0 + 0.4705882353 = 0.4705882353 -0.4117647059x + x2 = 0.4705882353 The x term is -0.4117647059x. Take half its coefficient (-0.205882353). Square it (0.04238754328) and add it to both sides. Add '0.04238754328' to each side of the equation. -0.4117647059x + 0.04238754328 + x2 = 0.4705882353 + 0.04238754328 Reorder the terms: 0.04238754328 + -0.4117647059x + x2 = 0.4705882353 + 0.04238754328 Combine like terms: 0.4705882353 + 0.04238754328 = 0.51297577858 0.04238754328 + -0.4117647059x + x2 = 0.51297577858 Factor a perfect square on the left side: (x + -0.205882353)(x + -0.205882353) = 0.51297577858 Calculate the square root of the right side: 0.716223274 Break this problem into two subproblems by setting (x + -0.205882353) equal to 0.716223274 and -0.716223274.Subproblem 1
x + -0.205882353 = 0.716223274 Simplifying x + -0.205882353 = 0.716223274 Reorder the terms: -0.205882353 + x = 0.716223274 Solving -0.205882353 + x = 0.716223274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.205882353' to each side of the equation. -0.205882353 + 0.205882353 + x = 0.716223274 + 0.205882353 Combine like terms: -0.205882353 + 0.205882353 = 0.000000000 0.000000000 + x = 0.716223274 + 0.205882353 x = 0.716223274 + 0.205882353 Combine like terms: 0.716223274 + 0.205882353 = 0.922105627 x = 0.922105627 Simplifying x = 0.922105627Subproblem 2
x + -0.205882353 = -0.716223274 Simplifying x + -0.205882353 = -0.716223274 Reorder the terms: -0.205882353 + x = -0.716223274 Solving -0.205882353 + x = -0.716223274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.205882353' to each side of the equation. -0.205882353 + 0.205882353 + x = -0.716223274 + 0.205882353 Combine like terms: -0.205882353 + 0.205882353 = 0.000000000 0.000000000 + x = -0.716223274 + 0.205882353 x = -0.716223274 + 0.205882353 Combine like terms: -0.716223274 + 0.205882353 = -0.510340921 x = -0.510340921 Simplifying x = -0.510340921Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.922105627, -0.510340921}
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