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Simplifying 0 = 0.2x + -0.003x2 + -1.4 Reorder the terms: 0 = -1.4 + 0.2x + -0.003x2 Solving 0 = -1.4 + 0.2x + -0.003x2 Solving for variable 'x'. Combine like terms: 0 + 1.4 = 1.4 1.4 + -0.2x + 0.003x2 = -1.4 + 0.2x + -0.003x2 + 1.4 + -0.2x + 0.003x2 Reorder the terms: 1.4 + -0.2x + 0.003x2 = -1.4 + 1.4 + 0.2x + -0.2x + -0.003x2 + 0.003x2 Combine like terms: -1.4 + 1.4 = 0.0 1.4 + -0.2x + 0.003x2 = 0.0 + 0.2x + -0.2x + -0.003x2 + 0.003x2 1.4 + -0.2x + 0.003x2 = 0.2x + -0.2x + -0.003x2 + 0.003x2 Combine like terms: 0.2x + -0.2x = 0.0 1.4 + -0.2x + 0.003x2 = 0.0 + -0.003x2 + 0.003x2 1.4 + -0.2x + 0.003x2 = -0.003x2 + 0.003x2 Combine like terms: -0.003x2 + 0.003x2 = 0.000 1.4 + -0.2x + 0.003x2 = 0.000 Begin completing the square. Divide all terms by 0.003 the coefficient of the squared term: Divide each side by '0.003'. 466.6666667 + -66.66666667x + x2 = 0 Move the constant term to the right: Add '-466.6666667' to each side of the equation. 466.6666667 + -66.66666667x + -466.6666667 + x2 = 0 + -466.6666667 Reorder the terms: 466.6666667 + -466.6666667 + -66.66666667x + x2 = 0 + -466.6666667 Combine like terms: 466.6666667 + -466.6666667 = 0.0000000 0.0000000 + -66.66666667x + x2 = 0 + -466.6666667 -66.66666667x + x2 = 0 + -466.6666667 Combine like terms: 0 + -466.6666667 = -466.6666667 -66.66666667x + x2 = -466.6666667 The x term is -66.66666667x. Take half its coefficient (-33.33333334). Square it (1111.111112) and add it to both sides. Add '1111.111112' to each side of the equation. -66.66666667x + 1111.111112 + x2 = -466.6666667 + 1111.111112 Reorder the terms: 1111.111112 + -66.66666667x + x2 = -466.6666667 + 1111.111112 Combine like terms: -466.6666667 + 1111.111112 = 644.4444453 1111.111112 + -66.66666667x + x2 = 644.4444453 Factor a perfect square on the left side: (x + -33.33333334)(x + -33.33333334) = 644.4444453 Calculate the square root of the right side: 25.38591037 Break this problem into two subproblems by setting (x + -33.33333334) equal to 25.38591037 and -25.38591037.Subproblem 1
x + -33.33333334 = 25.38591037 Simplifying x + -33.33333334 = 25.38591037 Reorder the terms: -33.33333334 + x = 25.38591037 Solving -33.33333334 + x = 25.38591037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = 25.38591037 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = 25.38591037 + 33.33333334 x = 25.38591037 + 33.33333334 Combine like terms: 25.38591037 + 33.33333334 = 58.71924371 x = 58.71924371 Simplifying x = 58.71924371Subproblem 2
x + -33.33333334 = -25.38591037 Simplifying x + -33.33333334 = -25.38591037 Reorder the terms: -33.33333334 + x = -25.38591037 Solving -33.33333334 + x = -25.38591037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = -25.38591037 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = -25.38591037 + 33.33333334 x = -25.38591037 + 33.33333334 Combine like terms: -25.38591037 + 33.33333334 = 7.94742297 x = 7.94742297 Simplifying x = 7.94742297Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.71924371, 7.94742297}
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