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Simplifying 2x(2x) + 12x = 7x + 42 Remove parenthesis around (2x) 2x * 2x + 12x = 7x + 42 Reorder the terms for easier multiplication: 2 * 2x * x + 12x = 7x + 42 Multiply 2 * 2 4x * x + 12x = 7x + 42 Multiply x * x 4x2 + 12x = 7x + 42 Reorder the terms: 12x + 4x2 = 7x + 42 Reorder the terms: 12x + 4x2 = 42 + 7x Solving 12x + 4x2 = 42 + 7x Solving for variable 'x'. Reorder the terms: -42 + 12x + -7x + 4x2 = 42 + 7x + -42 + -7x Combine like terms: 12x + -7x = 5x -42 + 5x + 4x2 = 42 + 7x + -42 + -7x Reorder the terms: -42 + 5x + 4x2 = 42 + -42 + 7x + -7x Combine like terms: 42 + -42 = 0 -42 + 5x + 4x2 = 0 + 7x + -7x -42 + 5x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -42 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.5 + 1.25x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 1.25x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 1.25x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 1.25x + x2 = 0 + 10.5 1.25x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 1.25x + x2 = 10.5 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 10.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 10.5 + 0.390625 Combine like terms: 10.5 + 0.390625 = 10.890625 0.390625 + 1.25x + x2 = 10.890625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 10.890625 Calculate the square root of the right side: 3.300094696 Break this problem into two subproblems by setting (x + 0.625) equal to 3.300094696 and -3.300094696.Subproblem 1
x + 0.625 = 3.300094696 Simplifying x + 0.625 = 3.300094696 Reorder the terms: 0.625 + x = 3.300094696 Solving 0.625 + x = 3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 3.300094696 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.300094696 + -0.625 x = 3.300094696 + -0.625 Combine like terms: 3.300094696 + -0.625 = 2.675094696 x = 2.675094696 Simplifying x = 2.675094696Subproblem 2
x + 0.625 = -3.300094696 Simplifying x + 0.625 = -3.300094696 Reorder the terms: 0.625 + x = -3.300094696 Solving 0.625 + x = -3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -3.300094696 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.300094696 + -0.625 x = -3.300094696 + -0.625 Combine like terms: -3.300094696 + -0.625 = -3.925094696 x = -3.925094696 Simplifying x = -3.925094696Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.675094696, -3.925094696}
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