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Simplifying x2 + 14x = 0.005 Reorder the terms: 14x + x2 = 0.005 Solving 14x + x2 = 0.005 Solving for variable 'x'. Reorder the terms: -0.005 + 14x + x2 = 0.005 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 -0.005 + 14x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.005' to each side of the equation. -0.005 + 14x + 0.005 + x2 = 0.000 + 0.005 Reorder the terms: -0.005 + 0.005 + 14x + x2 = 0.000 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + 14x + x2 = 0.000 + 0.005 14x + x2 = 0.000 + 0.005 Combine like terms: 0.000 + 0.005 = 0.005 14x + x2 = 0.005 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 0.005 + 49 Reorder the terms: 49 + 14x + x2 = 0.005 + 49 Combine like terms: 0.005 + 49 = 49.005 49 + 14x + x2 = 49.005 Factor a perfect square on the left side: (x + 7)(x + 7) = 49.005 Calculate the square root of the right side: 7.000357134 Break this problem into two subproblems by setting (x + 7) equal to 7.000357134 and -7.000357134.Subproblem 1
x + 7 = 7.000357134 Simplifying x + 7 = 7.000357134 Reorder the terms: 7 + x = 7.000357134 Solving 7 + x = 7.000357134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.000357134 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.000357134 + -7 x = 7.000357134 + -7 Combine like terms: 7.000357134 + -7 = 0.000357134 x = 0.000357134 Simplifying x = 0.000357134Subproblem 2
x + 7 = -7.000357134 Simplifying x + 7 = -7.000357134 Reorder the terms: 7 + x = -7.000357134 Solving 7 + x = -7.000357134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.000357134 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.000357134 + -7 x = -7.000357134 + -7 Combine like terms: -7.000357134 + -7 = -14.000357134 x = -14.000357134 Simplifying x = -14.000357134Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000357134, -14.000357134}
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