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Simplifying 3(x + -1) * 2x + 3 = 5x + 4(x + 10) Reorder the terms: 3(-1 + x) * 2x + 3 = 5x + 4(x + 10) Reorder the terms for easier multiplication: 3 * 2x(-1 + x) + 3 = 5x + 4(x + 10) Multiply 3 * 2 6x(-1 + x) + 3 = 5x + 4(x + 10) (-1 * 6x + x * 6x) + 3 = 5x + 4(x + 10) (-6x + 6x2) + 3 = 5x + 4(x + 10) Reorder the terms: 3 + -6x + 6x2 = 5x + 4(x + 10) Reorder the terms: 3 + -6x + 6x2 = 5x + 4(10 + x) 3 + -6x + 6x2 = 5x + (10 * 4 + x * 4) 3 + -6x + 6x2 = 5x + (40 + 4x) Reorder the terms: 3 + -6x + 6x2 = 40 + 5x + 4x Combine like terms: 5x + 4x = 9x 3 + -6x + 6x2 = 40 + 9x Solving 3 + -6x + 6x2 = 40 + 9x Solving for variable 'x'. Reorder the terms: 3 + -40 + -6x + -9x + 6x2 = 40 + 9x + -40 + -9x Combine like terms: 3 + -40 = -37 -37 + -6x + -9x + 6x2 = 40 + 9x + -40 + -9x Combine like terms: -6x + -9x = -15x -37 + -15x + 6x2 = 40 + 9x + -40 + -9x Reorder the terms: -37 + -15x + 6x2 = 40 + -40 + 9x + -9x Combine like terms: 40 + -40 = 0 -37 + -15x + 6x2 = 0 + 9x + -9x -37 + -15x + 6x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -37 + -15x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6.166666667 + -2.5x + x2 = 0 Move the constant term to the right: Add '6.166666667' to each side of the equation. -6.166666667 + -2.5x + 6.166666667 + x2 = 0 + 6.166666667 Reorder the terms: -6.166666667 + 6.166666667 + -2.5x + x2 = 0 + 6.166666667 Combine like terms: -6.166666667 + 6.166666667 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + 6.166666667 -2.5x + x2 = 0 + 6.166666667 Combine like terms: 0 + 6.166666667 = 6.166666667 -2.5x + x2 = 6.166666667 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 6.166666667 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 6.166666667 + 1.5625 Combine like terms: 6.166666667 + 1.5625 = 7.729166667 1.5625 + -2.5x + x2 = 7.729166667 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 7.729166667 Calculate the square root of the right side: 2.780137886 Break this problem into two subproblems by setting (x + -1.25) equal to 2.780137886 and -2.780137886.Subproblem 1
x + -1.25 = 2.780137886 Simplifying x + -1.25 = 2.780137886 Reorder the terms: -1.25 + x = 2.780137886 Solving -1.25 + x = 2.780137886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.780137886 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.780137886 + 1.25 x = 2.780137886 + 1.25 Combine like terms: 2.780137886 + 1.25 = 4.030137886 x = 4.030137886 Simplifying x = 4.030137886Subproblem 2
x + -1.25 = -2.780137886 Simplifying x + -1.25 = -2.780137886 Reorder the terms: -1.25 + x = -2.780137886 Solving -1.25 + x = -2.780137886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.780137886 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.780137886 + 1.25 x = -2.780137886 + 1.25 Combine like terms: -2.780137886 + 1.25 = -1.530137886 x = -1.530137886 Simplifying x = -1.530137886Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.030137886, -1.530137886}
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