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Simplifying 5x + -1[2x(5 + -3x)] * 7 = 1234 5x + -1[(5 * 2x + -3x * 2x)] * 7 = 1234 5x + -1[(10x + -6x2)] * 7 = 1234 Reorder the terms for easier multiplication: 5x + -1 * 7[10x + -6x2] = 1234 Multiply -1 * 7 5x + -7[10x + -6x2] = 1234 5x + [10x * -7 + -6x2 * -7] = 1234 5x + [-70x + 42x2] = 1234 Combine like terms: 5x + -70x = -65x -65x + 42x2 = 1234 Solving -65x + 42x2 = 1234 Solving for variable 'x'. Reorder the terms: -1234 + -65x + 42x2 = 1234 + -1234 Combine like terms: 1234 + -1234 = 0 -1234 + -65x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -29.38095238 + -1.547619048x + x2 = 0 Move the constant term to the right: Add '29.38095238' to each side of the equation. -29.38095238 + -1.547619048x + 29.38095238 + x2 = 0 + 29.38095238 Reorder the terms: -29.38095238 + 29.38095238 + -1.547619048x + x2 = 0 + 29.38095238 Combine like terms: -29.38095238 + 29.38095238 = 0.00000000 0.00000000 + -1.547619048x + x2 = 0 + 29.38095238 -1.547619048x + x2 = 0 + 29.38095238 Combine like terms: 0 + 29.38095238 = 29.38095238 -1.547619048x + x2 = 29.38095238 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 = 29.38095238 + 0.5987811794 Reorder the terms: 0.5987811794 + -1.547619048x + x2 = 29.38095238 + 0.5987811794 Combine like terms: 29.38095238 + 0.5987811794 = 29.9797335594 0.5987811794 + -1.547619048x + x2 = 29.9797335594 Factor a perfect square on the left side: (x + -0.773809524)(x + -0.773809524) = 29.9797335594 Calculate the square root of the right side: 5.475375198 Break this problem into two subproblems by setting (x + -0.773809524) equal to 5.475375198 and -5.475375198.Subproblem 1
x + -0.773809524 = 5.475375198 Simplifying x + -0.773809524 = 5.475375198 Reorder the terms: -0.773809524 + x = 5.475375198 Solving -0.773809524 + x = 5.475375198 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 = 5.475375198 + 0.773809524 Combine like terms: -0.773809524 + 0.773809524 = 0.000000000 0.000000000 + x = 5.475375198 + 0.773809524 x = 5.475375198 + 0.773809524 Combine like terms: 5.475375198 + 0.773809524 = 6.249184722 x = 6.249184722 Simplifying x = 6.249184722Subproblem 2
x + -0.773809524 = -5.475375198 Simplifying x + -0.773809524 = -5.475375198 Reorder the terms: -0.773809524 + x = -5.475375198 Solving -0.773809524 + x = -5.475375198 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 = -5.475375198 + 0.773809524 Combine like terms: -0.773809524 + 0.773809524 = 0.000000000 0.000000000 + x = -5.475375198 + 0.773809524 x = -5.475375198 + 0.773809524 Combine like terms: -5.475375198 + 0.773809524 = -4.701565674 x = -4.701565674 Simplifying x = -4.701565674Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.249184722, -4.701565674}
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