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Simplifying 2.1x + 6 = (1.5x + -0.24) * 1.4x Reorder the terms: 6 + 2.1x = (1.5x + -0.24) * 1.4x Reorder the terms: 6 + 2.1x = (-0.24 + 1.5x) * 1.4x Reorder the terms for easier multiplication: 6 + 2.1x = 1.4x(-0.24 + 1.5x) 6 + 2.1x = (-0.24 * 1.4x + 1.5x * 1.4x) 6 + 2.1x = (-0.336x + 2.1x2) Solving 6 + 2.1x = -0.336x + 2.1x2 Solving for variable 'x'. Combine like terms: 2.1x + 0.336x = 2.436x 6 + 2.436x + -2.1x2 = -0.336x + 2.1x2 + 0.336x + -2.1x2 Reorder the terms: 6 + 2.436x + -2.1x2 = -0.336x + 0.336x + 2.1x2 + -2.1x2 Combine like terms: -0.336x + 0.336x = 0.000 6 + 2.436x + -2.1x2 = 0.000 + 2.1x2 + -2.1x2 6 + 2.436x + -2.1x2 = 2.1x2 + -2.1x2 Combine like terms: 2.1x2 + -2.1x2 = 0.0 6 + 2.436x + -2.1x2 = 0.0 Begin completing the square. Divide all terms by -2.1 the coefficient of the squared term: Divide each side by '-2.1'. -2.857142857 + -1.16x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -1.16x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -1.16x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -1.16x + x2 = 0 + 2.857142857 -1.16x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -1.16x + x2 = 2.857142857 The x term is -1.16x. Take half its coefficient (-0.58). Square it (0.3364) and add it to both sides. Add '0.3364' to each side of the equation. -1.16x + 0.3364 + x2 = 2.857142857 + 0.3364 Reorder the terms: 0.3364 + -1.16x + x2 = 2.857142857 + 0.3364 Combine like terms: 2.857142857 + 0.3364 = 3.193542857 0.3364 + -1.16x + x2 = 3.193542857 Factor a perfect square on the left side: (x + -0.58)(x + -0.58) = 3.193542857 Calculate the square root of the right side: 1.787048644 Break this problem into two subproblems by setting (x + -0.58) equal to 1.787048644 and -1.787048644.Subproblem 1
x + -0.58 = 1.787048644 Simplifying x + -0.58 = 1.787048644 Reorder the terms: -0.58 + x = 1.787048644 Solving -0.58 + x = 1.787048644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.58' to each side of the equation. -0.58 + 0.58 + x = 1.787048644 + 0.58 Combine like terms: -0.58 + 0.58 = 0.00 0.00 + x = 1.787048644 + 0.58 x = 1.787048644 + 0.58 Combine like terms: 1.787048644 + 0.58 = 2.367048644 x = 2.367048644 Simplifying x = 2.367048644Subproblem 2
x + -0.58 = -1.787048644 Simplifying x + -0.58 = -1.787048644 Reorder the terms: -0.58 + x = -1.787048644 Solving -0.58 + x = -1.787048644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.58' to each side of the equation. -0.58 + 0.58 + x = -1.787048644 + 0.58 Combine like terms: -0.58 + 0.58 = 0.00 0.00 + x = -1.787048644 + 0.58 x = -1.787048644 + 0.58 Combine like terms: -1.787048644 + 0.58 = -1.207048644 x = -1.207048644 Simplifying x = -1.207048644Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.367048644, -1.207048644}
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