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Simplifying 5x(x + 0.4) = 2x + x + 14 Reorder the terms: 5x(0.4 + x) = 2x + x + 14 (0.4 * 5x + x * 5x) = 2x + x + 14 (2x + 5x2) = 2x + x + 14 Reorder the terms: 2x + 5x2 = 14 + 2x + x Combine like terms: 2x + x = 3x 2x + 5x2 = 14 + 3x Solving 2x + 5x2 = 14 + 3x Solving for variable 'x'. Reorder the terms: -14 + 2x + -3x + 5x2 = 14 + 3x + -14 + -3x Combine like terms: 2x + -3x = -1x -14 + -1x + 5x2 = 14 + 3x + -14 + -3x Reorder the terms: -14 + -1x + 5x2 = 14 + -14 + 3x + -3x Combine like terms: 14 + -14 = 0 -14 + -1x + 5x2 = 0 + 3x + -3x -14 + -1x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -14 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -0.2x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -0.2x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -0.2x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -0.2x + x2 = 0 + 2.8 -0.2x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -0.2x + x2 = 2.8 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 2.8 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 2.8 + 0.01 Combine like terms: 2.8 + 0.01 = 2.81 0.01 + -0.2x + x2 = 2.81 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 2.81 Calculate the square root of the right side: 1.676305461 Break this problem into two subproblems by setting (x + -0.1) equal to 1.676305461 and -1.676305461.Subproblem 1
x + -0.1 = 1.676305461 Simplifying x + -0.1 = 1.676305461 Reorder the terms: -0.1 + x = 1.676305461 Solving -0.1 + x = 1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.676305461 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.676305461 + 0.1 x = 1.676305461 + 0.1 Combine like terms: 1.676305461 + 0.1 = 1.776305461 x = 1.776305461 Simplifying x = 1.776305461Subproblem 2
x + -0.1 = -1.676305461 Simplifying x + -0.1 = -1.676305461 Reorder the terms: -0.1 + x = -1.676305461 Solving -0.1 + x = -1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.676305461 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.676305461 + 0.1 x = -1.676305461 + 0.1 Combine like terms: -1.676305461 + 0.1 = -1.576305461 x = -1.576305461 Simplifying x = -1.576305461Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.776305461, -1.576305461}
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