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Simplifying x2 = 15x + 326 Reorder the terms: x2 = 326 + 15x Solving x2 = 326 + 15x Solving for variable 'x'. Reorder the terms: -326 + -15x + x2 = 326 + 15x + -326 + -15x Reorder the terms: -326 + -15x + x2 = 326 + -326 + 15x + -15x Combine like terms: 326 + -326 = 0 -326 + -15x + x2 = 0 + 15x + -15x -326 + -15x + x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -326 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '326' to each side of the equation. -326 + -15x + 326 + x2 = 0 + 326 Reorder the terms: -326 + 326 + -15x + x2 = 0 + 326 Combine like terms: -326 + 326 = 0 0 + -15x + x2 = 0 + 326 -15x + x2 = 0 + 326 Combine like terms: 0 + 326 = 326 -15x + x2 = 326 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 326 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 326 + 56.25 Combine like terms: 326 + 56.25 = 382.25 56.25 + -15x + x2 = 382.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 382.25 Calculate the square root of the right side: 19.551214796 Break this problem into two subproblems by setting (x + -7.5) equal to 19.551214796 and -19.551214796.Subproblem 1
x + -7.5 = 19.551214796 Simplifying x + -7.5 = 19.551214796 Reorder the terms: -7.5 + x = 19.551214796 Solving -7.5 + x = 19.551214796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 19.551214796 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 19.551214796 + 7.5 x = 19.551214796 + 7.5 Combine like terms: 19.551214796 + 7.5 = 27.051214796 x = 27.051214796 Simplifying x = 27.051214796Subproblem 2
x + -7.5 = -19.551214796 Simplifying x + -7.5 = -19.551214796 Reorder the terms: -7.5 + x = -19.551214796 Solving -7.5 + x = -19.551214796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -19.551214796 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -19.551214796 + 7.5 x = -19.551214796 + 7.5 Combine like terms: -19.551214796 + 7.5 = -12.051214796 x = -12.051214796 Simplifying x = -12.051214796Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.051214796, -12.051214796}
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