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Simplifying -0.13x2 + 2.9x = 4 Reorder the terms: 2.9x + -0.13x2 = 4 Solving 2.9x + -0.13x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 2.9x + -0.13x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 2.9x + -0.13x2 = 0 Begin completing the square. Divide all terms by -0.13 the coefficient of the squared term: Divide each side by '-0.13'. 30.76923077 + -22.30769231x + x2 = 0 Move the constant term to the right: Add '-30.76923077' to each side of the equation. 30.76923077 + -22.30769231x + -30.76923077 + x2 = 0 + -30.76923077 Reorder the terms: 30.76923077 + -30.76923077 + -22.30769231x + x2 = 0 + -30.76923077 Combine like terms: 30.76923077 + -30.76923077 = 0.00000000 0.00000000 + -22.30769231x + x2 = 0 + -30.76923077 -22.30769231x + x2 = 0 + -30.76923077 Combine like terms: 0 + -30.76923077 = -30.76923077 -22.30769231x + x2 = -30.76923077 The x term is -22.30769231x. Take half its coefficient (-11.15384616). Square it (124.4082842) and add it to both sides. Add '124.4082842' to each side of the equation. -22.30769231x + 124.4082842 + x2 = -30.76923077 + 124.4082842 Reorder the terms: 124.4082842 + -22.30769231x + x2 = -30.76923077 + 124.4082842 Combine like terms: -30.76923077 + 124.4082842 = 93.63905343 124.4082842 + -22.30769231x + x2 = 93.63905343 Factor a perfect square on the left side: (x + -11.15384616)(x + -11.15384616) = 93.63905343 Calculate the square root of the right side: 9.676727413 Break this problem into two subproblems by setting (x + -11.15384616) equal to 9.676727413 and -9.676727413.Subproblem 1
x + -11.15384616 = 9.676727413 Simplifying x + -11.15384616 = 9.676727413 Reorder the terms: -11.15384616 + x = 9.676727413 Solving -11.15384616 + x = 9.676727413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.15384616' to each side of the equation. -11.15384616 + 11.15384616 + x = 9.676727413 + 11.15384616 Combine like terms: -11.15384616 + 11.15384616 = 0.00000000 0.00000000 + x = 9.676727413 + 11.15384616 x = 9.676727413 + 11.15384616 Combine like terms: 9.676727413 + 11.15384616 = 20.830573573 x = 20.830573573 Simplifying x = 20.830573573Subproblem 2
x + -11.15384616 = -9.676727413 Simplifying x + -11.15384616 = -9.676727413 Reorder the terms: -11.15384616 + x = -9.676727413 Solving -11.15384616 + x = -9.676727413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.15384616' to each side of the equation. -11.15384616 + 11.15384616 + x = -9.676727413 + 11.15384616 Combine like terms: -11.15384616 + 11.15384616 = 0.00000000 0.00000000 + x = -9.676727413 + 11.15384616 x = -9.676727413 + 11.15384616 Combine like terms: -9.676727413 + 11.15384616 = 1.477118747 x = 1.477118747 Simplifying x = 1.477118747Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.830573573, 1.477118747}
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