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Simplifying 14 = 0.01875x2 + 0.1575x + 1.5 Reorder the terms: 14 = 1.5 + 0.1575x + 0.01875x2 Solving 14 = 1.5 + 0.1575x + 0.01875x2 Solving for variable 'x'. Combine like terms: 14 + -1.5 = 12.5 12.5 + -0.1575x + -0.01875x2 = 1.5 + 0.1575x + 0.01875x2 + -1.5 + -0.1575x + -0.01875x2 Reorder the terms: 12.5 + -0.1575x + -0.01875x2 = 1.5 + -1.5 + 0.1575x + -0.1575x + 0.01875x2 + -0.01875x2 Combine like terms: 1.5 + -1.5 = 0.0 12.5 + -0.1575x + -0.01875x2 = 0.0 + 0.1575x + -0.1575x + 0.01875x2 + -0.01875x2 12.5 + -0.1575x + -0.01875x2 = 0.1575x + -0.1575x + 0.01875x2 + -0.01875x2 Combine like terms: 0.1575x + -0.1575x = 0.0000 12.5 + -0.1575x + -0.01875x2 = 0.0000 + 0.01875x2 + -0.01875x2 12.5 + -0.1575x + -0.01875x2 = 0.01875x2 + -0.01875x2 Combine like terms: 0.01875x2 + -0.01875x2 = 0.00000 12.5 + -0.1575x + -0.01875x2 = 0.00000 Begin completing the square. Divide all terms by -0.01875 the coefficient of the squared term: Divide each side by '-0.01875'. -666.6666667 + 8.4x + x2 = 0 Move the constant term to the right: Add '666.6666667' to each side of the equation. -666.6666667 + 8.4x + 666.6666667 + x2 = 0 + 666.6666667 Reorder the terms: -666.6666667 + 666.6666667 + 8.4x + x2 = 0 + 666.6666667 Combine like terms: -666.6666667 + 666.6666667 = 0.0000000 0.0000000 + 8.4x + x2 = 0 + 666.6666667 8.4x + x2 = 0 + 666.6666667 Combine like terms: 0 + 666.6666667 = 666.6666667 8.4x + x2 = 666.6666667 The x term is 8.4x. Take half its coefficient (4.2). Square it (17.64) and add it to both sides. Add '17.64' to each side of the equation. 8.4x + 17.64 + x2 = 666.6666667 + 17.64 Reorder the terms: 17.64 + 8.4x + x2 = 666.6666667 + 17.64 Combine like terms: 666.6666667 + 17.64 = 684.3066667 17.64 + 8.4x + x2 = 684.3066667 Factor a perfect square on the left side: (x + 4.2)(x + 4.2) = 684.3066667 Calculate the square root of the right side: 26.159255851 Break this problem into two subproblems by setting (x + 4.2) equal to 26.159255851 and -26.159255851.Subproblem 1
x + 4.2 = 26.159255851 Simplifying x + 4.2 = 26.159255851 Reorder the terms: 4.2 + x = 26.159255851 Solving 4.2 + x = 26.159255851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = 26.159255851 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = 26.159255851 + -4.2 x = 26.159255851 + -4.2 Combine like terms: 26.159255851 + -4.2 = 21.959255851 x = 21.959255851 Simplifying x = 21.959255851Subproblem 2
x + 4.2 = -26.159255851 Simplifying x + 4.2 = -26.159255851 Reorder the terms: 4.2 + x = -26.159255851 Solving 4.2 + x = -26.159255851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = -26.159255851 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = -26.159255851 + -4.2 x = -26.159255851 + -4.2 Combine like terms: -26.159255851 + -4.2 = -30.359255851 x = -30.359255851 Simplifying x = -30.359255851Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.959255851, -30.359255851}
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