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Simplifying 3x(2x + 2x) = 35 + 5x Combine like terms: 2x + 2x = 4x 3x(4x) = 35 + 5x Remove parenthesis around (4x) 3x * 4x = 35 + 5x Reorder the terms for easier multiplication: 3 * 4x * x = 35 + 5x Multiply 3 * 4 12x * x = 35 + 5x Multiply x * x 12x2 = 35 + 5x Solving 12x2 = 35 + 5x Solving for variable 'x'. Reorder the terms: -35 + -5x + 12x2 = 35 + 5x + -35 + -5x Reorder the terms: -35 + -5x + 12x2 = 35 + -35 + 5x + -5x Combine like terms: 35 + -35 = 0 -35 + -5x + 12x2 = 0 + 5x + -5x -35 + -5x + 12x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -35 + -5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.916666667 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '2.916666667' to each side of the equation. -2.916666667 + -0.4166666667x + 2.916666667 + x2 = 0 + 2.916666667 Reorder the terms: -2.916666667 + 2.916666667 + -0.4166666667x + x2 = 0 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + -0.4166666667x + x2 = 0 + 2.916666667 -0.4166666667x + x2 = 0 + 2.916666667 Combine like terms: 0 + 2.916666667 = 2.916666667 -0.4166666667x + x2 = 2.916666667 The x term is -0.4166666667x. Take half its coefficient (-0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. -0.4166666667x + 0.04340277781 + x2 = 2.916666667 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 2.916666667 + 0.04340277781 Combine like terms: 2.916666667 + 0.04340277781 = 2.96006944481 0.04340277781 + -0.4166666667x + x2 = 2.96006944481 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 2.96006944481 Calculate the square root of the right side: 1.720485235 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 1.720485235 and -1.720485235.Subproblem 1
x + -0.2083333334 = 1.720485235 Simplifying x + -0.2083333334 = 1.720485235 Reorder the terms: -0.2083333334 + x = 1.720485235 Solving -0.2083333334 + x = 1.720485235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = 1.720485235 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 1.720485235 + 0.2083333334 x = 1.720485235 + 0.2083333334 Combine like terms: 1.720485235 + 0.2083333334 = 1.9288185684 x = 1.9288185684 Simplifying x = 1.9288185684Subproblem 2
x + -0.2083333334 = -1.720485235 Simplifying x + -0.2083333334 = -1.720485235 Reorder the terms: -0.2083333334 + x = -1.720485235 Solving -0.2083333334 + x = -1.720485235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = -1.720485235 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -1.720485235 + 0.2083333334 x = -1.720485235 + 0.2083333334 Combine like terms: -1.720485235 + 0.2083333334 = -1.5121519016 x = -1.5121519016 Simplifying x = -1.5121519016Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9288185684, -1.5121519016}
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