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Simplifying 17x2 + 25x + -10 = 0 Reorder the terms: -10 + 25x + 17x2 = 0 Solving -10 + 25x + 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'. -0.5882352941 + 1.470588235x + x2 = 0 Move the constant term to the right: Add '0.5882352941' to each side of the equation. -0.5882352941 + 1.470588235x + 0.5882352941 + x2 = 0 + 0.5882352941 Reorder the terms: -0.5882352941 + 0.5882352941 + 1.470588235x + x2 = 0 + 0.5882352941 Combine like terms: -0.5882352941 + 0.5882352941 = 0.0000000000 0.0000000000 + 1.470588235x + x2 = 0 + 0.5882352941 1.470588235x + x2 = 0 + 0.5882352941 Combine like terms: 0 + 0.5882352941 = 0.5882352941 1.470588235x + x2 = 0.5882352941 The x term is 1.470588235x. Take half its coefficient (0.7352941175). Square it (0.5406574392) and add it to both sides. Add '0.5406574392' to each side of the equation. 1.470588235x + 0.5406574392 + x2 = 0.5882352941 + 0.5406574392 Reorder the terms: 0.5406574392 + 1.470588235x + x2 = 0.5882352941 + 0.5406574392 Combine like terms: 0.5882352941 + 0.5406574392 = 1.1288927333 0.5406574392 + 1.470588235x + x2 = 1.1288927333 Factor a perfect square on the left side: (x + 0.7352941175)(x + 0.7352941175) = 1.1288927333 Calculate the square root of the right side: 1.062493639 Break this problem into two subproblems by setting (x + 0.7352941175) equal to 1.062493639 and -1.062493639.Subproblem 1
x + 0.7352941175 = 1.062493639 Simplifying x + 0.7352941175 = 1.062493639 Reorder the terms: 0.7352941175 + x = 1.062493639 Solving 0.7352941175 + x = 1.062493639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7352941175' to each side of the equation. 0.7352941175 + -0.7352941175 + x = 1.062493639 + -0.7352941175 Combine like terms: 0.7352941175 + -0.7352941175 = 0.0000000000 0.0000000000 + x = 1.062493639 + -0.7352941175 x = 1.062493639 + -0.7352941175 Combine like terms: 1.062493639 + -0.7352941175 = 0.3271995215 x = 0.3271995215 Simplifying x = 0.3271995215Subproblem 2
x + 0.7352941175 = -1.062493639 Simplifying x + 0.7352941175 = -1.062493639 Reorder the terms: 0.7352941175 + x = -1.062493639 Solving 0.7352941175 + x = -1.062493639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7352941175' to each side of the equation. 0.7352941175 + -0.7352941175 + x = -1.062493639 + -0.7352941175 Combine like terms: 0.7352941175 + -0.7352941175 = 0.0000000000 0.0000000000 + x = -1.062493639 + -0.7352941175 x = -1.062493639 + -0.7352941175 Combine like terms: -1.062493639 + -0.7352941175 = -1.7977877565 x = -1.7977877565 Simplifying x = -1.7977877565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3271995215, -1.7977877565}
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