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Simplifying x2 + 0.14x = 150 Reorder the terms: 0.14x + x2 = 150 Solving 0.14x + x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 0.14x + x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 0.14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 0.14x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 0.14x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 0.14x + x2 = 0 + 150 0.14x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 0.14x + x2 = 150 The x term is 0.14x. Take half its coefficient (0.07). Square it (0.0049) and add it to both sides. Add '0.0049' to each side of the equation. 0.14x + 0.0049 + x2 = 150 + 0.0049 Reorder the terms: 0.0049 + 0.14x + x2 = 150 + 0.0049 Combine like terms: 150 + 0.0049 = 150.0049 0.0049 + 0.14x + x2 = 150.0049 Factor a perfect square on the left side: (x + 0.07)(x + 0.07) = 150.0049 Calculate the square root of the right side: 12.247648754 Break this problem into two subproblems by setting (x + 0.07) equal to 12.247648754 and -12.247648754.Subproblem 1
x + 0.07 = 12.247648754 Simplifying x + 0.07 = 12.247648754 Reorder the terms: 0.07 + x = 12.247648754 Solving 0.07 + x = 12.247648754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07' to each side of the equation. 0.07 + -0.07 + x = 12.247648754 + -0.07 Combine like terms: 0.07 + -0.07 = 0.00 0.00 + x = 12.247648754 + -0.07 x = 12.247648754 + -0.07 Combine like terms: 12.247648754 + -0.07 = 12.177648754 x = 12.177648754 Simplifying x = 12.177648754Subproblem 2
x + 0.07 = -12.247648754 Simplifying x + 0.07 = -12.247648754 Reorder the terms: 0.07 + x = -12.247648754 Solving 0.07 + x = -12.247648754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07' to each side of the equation. 0.07 + -0.07 + x = -12.247648754 + -0.07 Combine like terms: 0.07 + -0.07 = 0.00 0.00 + x = -12.247648754 + -0.07 x = -12.247648754 + -0.07 Combine like terms: -12.247648754 + -0.07 = -12.317648754 x = -12.317648754 Simplifying x = -12.317648754Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.177648754, -12.317648754}
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