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Simplifying 2x + 5 = 5x2 + -37 Reorder the terms: 5 + 2x = 5x2 + -37 Reorder the terms: 5 + 2x = -37 + 5x2 Solving 5 + 2x = -37 + 5x2 Solving for variable 'x'. Reorder the terms: 5 + 37 + 2x + -5x2 = -37 + 5x2 + 37 + -5x2 Combine like terms: 5 + 37 = 42 42 + 2x + -5x2 = -37 + 5x2 + 37 + -5x2 Reorder the terms: 42 + 2x + -5x2 = -37 + 37 + 5x2 + -5x2 Combine like terms: -37 + 37 = 0 42 + 2x + -5x2 = 0 + 5x2 + -5x2 42 + 2x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 42 + 2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8.4 + -0.4x + x2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + -0.4x + 8.4 + x2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + -0.4x + x2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + -0.4x + x2 = 0 + 8.4 -0.4x + x2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 -0.4x + x2 = 8.4 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 8.4 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 8.4 + 0.04 Combine like terms: 8.4 + 0.04 = 8.44 0.04 + -0.4x + x2 = 8.44 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 8.44 Calculate the square root of the right side: 2.905167809 Break this problem into two subproblems by setting (x + -0.2) equal to 2.905167809 and -2.905167809.Subproblem 1
x + -0.2 = 2.905167809 Simplifying x + -0.2 = 2.905167809 Reorder the terms: -0.2 + x = 2.905167809 Solving -0.2 + x = 2.905167809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 2.905167809 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 2.905167809 + 0.2 x = 2.905167809 + 0.2 Combine like terms: 2.905167809 + 0.2 = 3.105167809 x = 3.105167809 Simplifying x = 3.105167809Subproblem 2
x + -0.2 = -2.905167809 Simplifying x + -0.2 = -2.905167809 Reorder the terms: -0.2 + x = -2.905167809 Solving -0.2 + x = -2.905167809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -2.905167809 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -2.905167809 + 0.2 x = -2.905167809 + 0.2 Combine like terms: -2.905167809 + 0.2 = -2.705167809 x = -2.705167809 Simplifying x = -2.705167809Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.105167809, -2.705167809}
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