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Simplifying 0 = -0.006x2 + 2.5x + 4 Reorder the terms: 0 = 4 + 2.5x + -0.006x2 Solving 0 = 4 + 2.5x + -0.006x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -2.5x + 0.006x2 = 4 + 2.5x + -0.006x2 + -4 + -2.5x + 0.006x2 Reorder the terms: -4 + -2.5x + 0.006x2 = 4 + -4 + 2.5x + -2.5x + -0.006x2 + 0.006x2 Combine like terms: 4 + -4 = 0 -4 + -2.5x + 0.006x2 = 0 + 2.5x + -2.5x + -0.006x2 + 0.006x2 -4 + -2.5x + 0.006x2 = 2.5x + -2.5x + -0.006x2 + 0.006x2 Combine like terms: 2.5x + -2.5x = 0.0 -4 + -2.5x + 0.006x2 = 0.0 + -0.006x2 + 0.006x2 -4 + -2.5x + 0.006x2 = -0.006x2 + 0.006x2 Combine like terms: -0.006x2 + 0.006x2 = 0.000 -4 + -2.5x + 0.006x2 = 0.000 Begin completing the square. Divide all terms by 0.006 the coefficient of the squared term: Divide each side by '0.006'. -666.6666667 + -416.6666667x + x2 = 0 Move the constant term to the right: Add '666.6666667' to each side of the equation. -666.6666667 + -416.6666667x + 666.6666667 + x2 = 0 + 666.6666667 Reorder the terms: -666.6666667 + 666.6666667 + -416.6666667x + x2 = 0 + 666.6666667 Combine like terms: -666.6666667 + 666.6666667 = 0.0000000 0.0000000 + -416.6666667x + x2 = 0 + 666.6666667 -416.6666667x + x2 = 0 + 666.6666667 Combine like terms: 0 + 666.6666667 = 666.6666667 -416.6666667x + x2 = 666.6666667 The x term is -416.6666667x. Take half its coefficient (-208.3333334). Square it (43402.77781) and add it to both sides. Add '43402.77781' to each side of the equation. -416.6666667x + 43402.77781 + x2 = 666.6666667 + 43402.77781 Reorder the terms: 43402.77781 + -416.6666667x + x2 = 666.6666667 + 43402.77781 Combine like terms: 666.6666667 + 43402.77781 = 44069.4444767 43402.77781 + -416.6666667x + x2 = 44069.4444767 Factor a perfect square on the left side: (x + -208.3333334)(x + -208.3333334) = 44069.4444767 Calculate the square root of the right side: 209.927236148 Break this problem into two subproblems by setting (x + -208.3333334) equal to 209.927236148 and -209.927236148.Subproblem 1
x + -208.3333334 = 209.927236148 Simplifying x + -208.3333334 = 209.927236148 Reorder the terms: -208.3333334 + x = 209.927236148 Solving -208.3333334 + x = 209.927236148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '208.3333334' to each side of the equation. -208.3333334 + 208.3333334 + x = 209.927236148 + 208.3333334 Combine like terms: -208.3333334 + 208.3333334 = 0.0000000 0.0000000 + x = 209.927236148 + 208.3333334 x = 209.927236148 + 208.3333334 Combine like terms: 209.927236148 + 208.3333334 = 418.260569548 x = 418.260569548 Simplifying x = 418.260569548Subproblem 2
x + -208.3333334 = -209.927236148 Simplifying x + -208.3333334 = -209.927236148 Reorder the terms: -208.3333334 + x = -209.927236148 Solving -208.3333334 + x = -209.927236148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '208.3333334' to each side of the equation. -208.3333334 + 208.3333334 + x = -209.927236148 + 208.3333334 Combine like terms: -208.3333334 + 208.3333334 = 0.0000000 0.0000000 + x = -209.927236148 + 208.3333334 x = -209.927236148 + 208.3333334 Combine like terms: -209.927236148 + 208.3333334 = -1.593902748 x = -1.593902748 Simplifying x = -1.593902748Solution
The solution to the problem is based on the solutions from the subproblems. x = {418.260569548, -1.593902748}
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