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Simplifying x2 + 14x = 0.004 Reorder the terms: 14x + x2 = 0.004 Solving 14x + x2 = 0.004 Solving for variable 'x'. Reorder the terms: -0.004 + 14x + x2 = 0.004 + -0.004 Combine like terms: 0.004 + -0.004 = 0.000 -0.004 + 14x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.004' to each side of the equation. -0.004 + 14x + 0.004 + x2 = 0.000 + 0.004 Reorder the terms: -0.004 + 0.004 + 14x + x2 = 0.000 + 0.004 Combine like terms: -0.004 + 0.004 = 0.000 0.000 + 14x + x2 = 0.000 + 0.004 14x + x2 = 0.000 + 0.004 Combine like terms: 0.000 + 0.004 = 0.004 14x + x2 = 0.004 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 = 0.004 + 49 Reorder the terms: 49 + 14x + x2 = 0.004 + 49 Combine like terms: 0.004 + 49 = 49.004 49 + 14x + x2 = 49.004 Factor a perfect square on the left side: (x + 7)(x + 7) = 49.004 Calculate the square root of the right side: 7.000285708 Break this problem into two subproblems by setting (x + 7) equal to 7.000285708 and -7.000285708.Subproblem 1
x + 7 = 7.000285708 Simplifying x + 7 = 7.000285708 Reorder the terms: 7 + x = 7.000285708 Solving 7 + x = 7.000285708 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 = 7.000285708 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.000285708 + -7 x = 7.000285708 + -7 Combine like terms: 7.000285708 + -7 = 0.000285708 x = 0.000285708 Simplifying x = 0.000285708Subproblem 2
x + 7 = -7.000285708 Simplifying x + 7 = -7.000285708 Reorder the terms: 7 + x = -7.000285708 Solving 7 + x = -7.000285708 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 = -7.000285708 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.000285708 + -7 x = -7.000285708 + -7 Combine like terms: -7.000285708 + -7 = -14.000285708 x = -14.000285708 Simplifying x = -14.000285708Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000285708, -14.000285708}
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