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Simplifying 17x2 + -2x + -75 = 0 Reorder the terms: -75 + -2x + 17x2 = 0 Solving -75 + -2x + 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'. -4.411764706 + -0.1176470588x + x2 = 0 Move the constant term to the right: Add '4.411764706' to each side of the equation. -4.411764706 + -0.1176470588x + 4.411764706 + x2 = 0 + 4.411764706 Reorder the terms: -4.411764706 + 4.411764706 + -0.1176470588x + x2 = 0 + 4.411764706 Combine like terms: -4.411764706 + 4.411764706 = 0.000000000 0.000000000 + -0.1176470588x + x2 = 0 + 4.411764706 -0.1176470588x + x2 = 0 + 4.411764706 Combine like terms: 0 + 4.411764706 = 4.411764706 -0.1176470588x + x2 = 4.411764706 The x term is -0.1176470588x. Take half its coefficient (-0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. -0.1176470588x + 0.003460207611 + x2 = 4.411764706 + 0.003460207611 Reorder the terms: 0.003460207611 + -0.1176470588x + x2 = 4.411764706 + 0.003460207611 Combine like terms: 4.411764706 + 0.003460207611 = 4.415224913611 0.003460207611 + -0.1176470588x + x2 = 4.415224913611 Factor a perfect square on the left side: (x + -0.0588235294)(x + -0.0588235294) = 4.415224913611 Calculate the square root of the right side: 2.101243659 Break this problem into two subproblems by setting (x + -0.0588235294) equal to 2.101243659 and -2.101243659.Subproblem 1
x + -0.0588235294 = 2.101243659 Simplifying x + -0.0588235294 = 2.101243659 Reorder the terms: -0.0588235294 + x = 2.101243659 Solving -0.0588235294 + x = 2.101243659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0588235294' to each side of the equation. -0.0588235294 + 0.0588235294 + x = 2.101243659 + 0.0588235294 Combine like terms: -0.0588235294 + 0.0588235294 = 0.0000000000 0.0000000000 + x = 2.101243659 + 0.0588235294 x = 2.101243659 + 0.0588235294 Combine like terms: 2.101243659 + 0.0588235294 = 2.1600671884 x = 2.1600671884 Simplifying x = 2.1600671884Subproblem 2
x + -0.0588235294 = -2.101243659 Simplifying x + -0.0588235294 = -2.101243659 Reorder the terms: -0.0588235294 + x = -2.101243659 Solving -0.0588235294 + x = -2.101243659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0588235294' to each side of the equation. -0.0588235294 + 0.0588235294 + x = -2.101243659 + 0.0588235294 Combine like terms: -0.0588235294 + 0.0588235294 = 0.0000000000 0.0000000000 + x = -2.101243659 + 0.0588235294 x = -2.101243659 + 0.0588235294 Combine like terms: -2.101243659 + 0.0588235294 = -2.0424201296 x = -2.0424201296 Simplifying x = -2.0424201296Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1600671884, -2.0424201296}
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