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Simplifying (x + -2.9)(x + 1.4) = 0 Reorder the terms: (-2.9 + x)(x + 1.4) = 0 Reorder the terms: (-2.9 + x)(1.4 + x) = 0 Multiply (-2.9 + x) * (1.4 + x) (-2.9(1.4 + x) + x(1.4 + x)) = 0 ((1.4 * -2.9 + x * -2.9) + x(1.4 + x)) = 0 ((-4.06 + -2.9x) + x(1.4 + x)) = 0 (-4.06 + -2.9x + (1.4 * x + x * x)) = 0 (-4.06 + -2.9x + (1.4x + x2)) = 0 Combine like terms: -2.9x + 1.4x = -1.5x (-4.06 + -1.5x + x2) = 0 Solving -4.06 + -1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4.06' to each side of the equation. -4.06 + -1.5x + 4.06 + x2 = 0 + 4.06 Reorder the terms: -4.06 + 4.06 + -1.5x + x2 = 0 + 4.06 Combine like terms: -4.06 + 4.06 = 0.00 0.00 + -1.5x + x2 = 0 + 4.06 -1.5x + x2 = 0 + 4.06 Combine like terms: 0 + 4.06 = 4.06 -1.5x + x2 = 4.06 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 4.06 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 4.06 + 0.5625 Combine like terms: 4.06 + 0.5625 = 4.6225 0.5625 + -1.5x + x2 = 4.6225 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 4.6225 Calculate the square root of the right side: 2.15 Break this problem into two subproblems by setting (x + -0.75) equal to 2.15 and -2.15.Subproblem 1
x + -0.75 = 2.15 Simplifying x + -0.75 = 2.15 Reorder the terms: -0.75 + x = 2.15 Solving -0.75 + x = 2.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.15 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.15 + 0.75 x = 2.15 + 0.75 Combine like terms: 2.15 + 0.75 = 2.9 x = 2.9 Simplifying x = 2.9Subproblem 2
x + -0.75 = -2.15 Simplifying x + -0.75 = -2.15 Reorder the terms: -0.75 + x = -2.15 Solving -0.75 + x = -2.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.15 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.15 + 0.75 x = -2.15 + 0.75 Combine like terms: -2.15 + 0.75 = -1.4 x = -1.4 Simplifying x = -1.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9, -1.4}
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