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Simplifying x2 + -15x + -336 = 0 Reorder the terms: -336 + -15x + x2 = 0 Solving -336 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '336' to each side of the equation. -336 + -15x + 336 + x2 = 0 + 336 Reorder the terms: -336 + 336 + -15x + x2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + -15x + x2 = 0 + 336 -15x + x2 = 0 + 336 Combine like terms: 0 + 336 = 336 -15x + x2 = 336 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 = 336 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 336 + 56.25 Combine like terms: 336 + 56.25 = 392.25 56.25 + -15x + x2 = 392.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 392.25 Calculate the square root of the right side: 19.80530232 Break this problem into two subproblems by setting (x + -7.5) equal to 19.80530232 and -19.80530232.Subproblem 1
x + -7.5 = 19.80530232 Simplifying x + -7.5 = 19.80530232 Reorder the terms: -7.5 + x = 19.80530232 Solving -7.5 + x = 19.80530232 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 = 19.80530232 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 19.80530232 + 7.5 x = 19.80530232 + 7.5 Combine like terms: 19.80530232 + 7.5 = 27.30530232 x = 27.30530232 Simplifying x = 27.30530232Subproblem 2
x + -7.5 = -19.80530232 Simplifying x + -7.5 = -19.80530232 Reorder the terms: -7.5 + x = -19.80530232 Solving -7.5 + x = -19.80530232 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 = -19.80530232 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -19.80530232 + 7.5 x = -19.80530232 + 7.5 Combine like terms: -19.80530232 + 7.5 = -12.30530232 x = -12.30530232 Simplifying x = -12.30530232Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.30530232, -12.30530232}
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