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Simplifying 12x * 4x + 5 = 5x + 7 Reorder the terms for easier multiplication: 12 * 4x * x + 5 = 5x + 7 Multiply 12 * 4 48x * x + 5 = 5x + 7 Multiply x * x 48x2 + 5 = 5x + 7 Reorder the terms: 5 + 48x2 = 5x + 7 Reorder the terms: 5 + 48x2 = 7 + 5x Solving 5 + 48x2 = 7 + 5x Solving for variable 'x'. Reorder the terms: 5 + -7 + -5x + 48x2 = 7 + 5x + -7 + -5x Combine like terms: 5 + -7 = -2 -2 + -5x + 48x2 = 7 + 5x + -7 + -5x Reorder the terms: -2 + -5x + 48x2 = 7 + -7 + 5x + -5x Combine like terms: 7 + -7 = 0 -2 + -5x + 48x2 = 0 + 5x + -5x -2 + -5x + 48x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -2 + -5x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.04166666667 + -0.1041666667x + x2 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -0.1041666667x + 0.04166666667 + x2 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -0.1041666667x + x2 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -0.1041666667x + x2 = 0 + 0.04166666667 -0.1041666667x + x2 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -0.1041666667x + x2 = 0.04166666667 The x term is -0.1041666667x. Take half its coefficient (-0.05208333335). Square it (0.002712673613) and add it to both sides. Add '0.002712673613' to each side of the equation. -0.1041666667x + 0.002712673613 + x2 = 0.04166666667 + 0.002712673613 Reorder the terms: 0.002712673613 + -0.1041666667x + x2 = 0.04166666667 + 0.002712673613 Combine like terms: 0.04166666667 + 0.002712673613 = 0.044379340283 0.002712673613 + -0.1041666667x + x2 = 0.044379340283 Factor a perfect square on the left side: (x + -0.05208333335)(x + -0.05208333335) = 0.044379340283 Calculate the square root of the right side: 0.210664046 Break this problem into two subproblems by setting (x + -0.05208333335) equal to 0.210664046 and -0.210664046.Subproblem 1
x + -0.05208333335 = 0.210664046 Simplifying x + -0.05208333335 = 0.210664046 Reorder the terms: -0.05208333335 + x = 0.210664046 Solving -0.05208333335 + x = 0.210664046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05208333335' to each side of the equation. -0.05208333335 + 0.05208333335 + x = 0.210664046 + 0.05208333335 Combine like terms: -0.05208333335 + 0.05208333335 = 0.00000000000 0.00000000000 + x = 0.210664046 + 0.05208333335 x = 0.210664046 + 0.05208333335 Combine like terms: 0.210664046 + 0.05208333335 = 0.26274737935 x = 0.26274737935 Simplifying x = 0.26274737935Subproblem 2
x + -0.05208333335 = -0.210664046 Simplifying x + -0.05208333335 = -0.210664046 Reorder the terms: -0.05208333335 + x = -0.210664046 Solving -0.05208333335 + x = -0.210664046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05208333335' to each side of the equation. -0.05208333335 + 0.05208333335 + x = -0.210664046 + 0.05208333335 Combine like terms: -0.05208333335 + 0.05208333335 = 0.00000000000 0.00000000000 + x = -0.210664046 + 0.05208333335 x = -0.210664046 + 0.05208333335 Combine like terms: -0.210664046 + 0.05208333335 = -0.15858071265 x = -0.15858071265 Simplifying x = -0.15858071265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.26274737935, -0.15858071265}
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