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Simplifying x2 + -12x + -9564 = 0 Reorder the terms: -9564 + -12x + x2 = 0 Solving -9564 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9564' to each side of the equation. -9564 + -12x + 9564 + x2 = 0 + 9564 Reorder the terms: -9564 + 9564 + -12x + x2 = 0 + 9564 Combine like terms: -9564 + 9564 = 0 0 + -12x + x2 = 0 + 9564 -12x + x2 = 0 + 9564 Combine like terms: 0 + 9564 = 9564 -12x + x2 = 9564 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 9564 + 36 Reorder the terms: 36 + -12x + x2 = 9564 + 36 Combine like terms: 9564 + 36 = 9600 36 + -12x + x2 = 9600 Factor a perfect square on the left side: (x + -6)(x + -6) = 9600 Calculate the square root of the right side: 97.979589711 Break this problem into two subproblems by setting (x + -6) equal to 97.979589711 and -97.979589711.Subproblem 1
x + -6 = 97.979589711 Simplifying x + -6 = 97.979589711 Reorder the terms: -6 + x = 97.979589711 Solving -6 + x = 97.979589711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 97.979589711 + 6 Combine like terms: -6 + 6 = 0 0 + x = 97.979589711 + 6 x = 97.979589711 + 6 Combine like terms: 97.979589711 + 6 = 103.979589711 x = 103.979589711 Simplifying x = 103.979589711Subproblem 2
x + -6 = -97.979589711 Simplifying x + -6 = -97.979589711 Reorder the terms: -6 + x = -97.979589711 Solving -6 + x = -97.979589711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -97.979589711 + 6 Combine like terms: -6 + 6 = 0 0 + x = -97.979589711 + 6 x = -97.979589711 + 6 Combine like terms: -97.979589711 + 6 = -91.979589711 x = -91.979589711 Simplifying x = -91.979589711Solution
The solution to the problem is based on the solutions from the subproblems. x = {103.979589711, -91.979589711}
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