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Simplifying 5x + -1[2x(5 + -3x)] * 7 = 12345 5x + -1[(5 * 2x + -3x * 2x)] * 7 = 12345 5x + -1[(10x + -6x2)] * 7 = 12345 Reorder the terms for easier multiplication: 5x + -1 * 7[10x + -6x2] = 12345 Multiply -1 * 7 5x + -7[10x + -6x2] = 12345 5x + [10x * -7 + -6x2 * -7] = 12345 5x + [-70x + 42x2] = 12345 Combine like terms: 5x + -70x = -65x -65x + 42x2 = 12345 Solving -65x + 42x2 = 12345 Solving for variable 'x'. Reorder the terms: -12345 + -65x + 42x2 = 12345 + -12345 Combine like terms: 12345 + -12345 = 0 -12345 + -65x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -293.9285714 + -1.547619048x + x2 = 0 Move the constant term to the right: Add '293.9285714' to each side of the equation. -293.9285714 + -1.547619048x + 293.9285714 + x2 = 0 + 293.9285714 Reorder the terms: -293.9285714 + 293.9285714 + -1.547619048x + x2 = 0 + 293.9285714 Combine like terms: -293.9285714 + 293.9285714 = 0.0000000 0.0000000 + -1.547619048x + x2 = 0 + 293.9285714 -1.547619048x + x2 = 0 + 293.9285714 Combine like terms: 0 + 293.9285714 = 293.9285714 -1.547619048x + x2 = 293.9285714 The x term is -1.547619048x. Take half its coefficient (-0.773809524). Square it (0.5987811794) and add it to both sides. Add '0.5987811794' to each side of the equation. -1.547619048x + 0.5987811794 + x2 = 293.9285714 + 0.5987811794 Reorder the terms: 0.5987811794 + -1.547619048x + x2 = 293.9285714 + 0.5987811794 Combine like terms: 293.9285714 + 0.5987811794 = 294.5273525794 0.5987811794 + -1.547619048x + x2 = 294.5273525794 Factor a perfect square on the left side: (x + -0.773809524)(x + -0.773809524) = 294.5273525794 Calculate the square root of the right side: 17.161799223 Break this problem into two subproblems by setting (x + -0.773809524) equal to 17.161799223 and -17.161799223.Subproblem 1
x + -0.773809524 = 17.161799223 Simplifying x + -0.773809524 = 17.161799223 Reorder the terms: -0.773809524 + x = 17.161799223 Solving -0.773809524 + x = 17.161799223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.773809524' to each side of the equation. -0.773809524 + 0.773809524 + x = 17.161799223 + 0.773809524 Combine like terms: -0.773809524 + 0.773809524 = 0.000000000 0.000000000 + x = 17.161799223 + 0.773809524 x = 17.161799223 + 0.773809524 Combine like terms: 17.161799223 + 0.773809524 = 17.935608747 x = 17.935608747 Simplifying x = 17.935608747Subproblem 2
x + -0.773809524 = -17.161799223 Simplifying x + -0.773809524 = -17.161799223 Reorder the terms: -0.773809524 + x = -17.161799223 Solving -0.773809524 + x = -17.161799223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.773809524' to each side of the equation. -0.773809524 + 0.773809524 + x = -17.161799223 + 0.773809524 Combine like terms: -0.773809524 + 0.773809524 = 0.000000000 0.000000000 + x = -17.161799223 + 0.773809524 x = -17.161799223 + 0.773809524 Combine like terms: -17.161799223 + 0.773809524 = -16.387989699 x = -16.387989699 Simplifying x = -16.387989699Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.935608747, -16.387989699}
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