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Simplifying -0.012x2 + 4.2x + -30 = 0 Reorder the terms: -30 + 4.2x + -0.012x2 = 0 Solving -30 + 4.2x + -0.012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.012 the coefficient of the squared term: Divide each side by '-0.012'. 2500 + -350x + x2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -350x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -350x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -350x + x2 = 0 + -2500 -350x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -350x + x2 = -2500 The x term is -350x. Take half its coefficient (-175). Square it (30625) and add it to both sides. Add '30625' to each side of the equation. -350x + 30625 + x2 = -2500 + 30625 Reorder the terms: 30625 + -350x + x2 = -2500 + 30625 Combine like terms: -2500 + 30625 = 28125 30625 + -350x + x2 = 28125 Factor a perfect square on the left side: (x + -175)(x + -175) = 28125 Calculate the square root of the right side: 167.705098312 Break this problem into two subproblems by setting (x + -175) equal to 167.705098312 and -167.705098312.Subproblem 1
x + -175 = 167.705098312 Simplifying x + -175 = 167.705098312 Reorder the terms: -175 + x = 167.705098312 Solving -175 + x = 167.705098312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '175' to each side of the equation. -175 + 175 + x = 167.705098312 + 175 Combine like terms: -175 + 175 = 0 0 + x = 167.705098312 + 175 x = 167.705098312 + 175 Combine like terms: 167.705098312 + 175 = 342.705098312 x = 342.705098312 Simplifying x = 342.705098312Subproblem 2
x + -175 = -167.705098312 Simplifying x + -175 = -167.705098312 Reorder the terms: -175 + x = -167.705098312 Solving -175 + x = -167.705098312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '175' to each side of the equation. -175 + 175 + x = -167.705098312 + 175 Combine like terms: -175 + 175 = 0 0 + x = -167.705098312 + 175 x = -167.705098312 + 175 Combine like terms: -167.705098312 + 175 = 7.294901688 x = 7.294901688 Simplifying x = 7.294901688Solution
The solution to the problem is based on the solutions from the subproblems. x = {342.705098312, 7.294901688}
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