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Simplifying 0 = -2.7x2 + 32x + 5 Reorder the terms: 0 = 5 + 32x + -2.7x2 Solving 0 = 5 + 32x + -2.7x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -32x + 2.7x2 = 5 + 32x + -2.7x2 + -5 + -32x + 2.7x2 Reorder the terms: -5 + -32x + 2.7x2 = 5 + -5 + 32x + -32x + -2.7x2 + 2.7x2 Combine like terms: 5 + -5 = 0 -5 + -32x + 2.7x2 = 0 + 32x + -32x + -2.7x2 + 2.7x2 -5 + -32x + 2.7x2 = 32x + -32x + -2.7x2 + 2.7x2 Combine like terms: 32x + -32x = 0 -5 + -32x + 2.7x2 = 0 + -2.7x2 + 2.7x2 -5 + -32x + 2.7x2 = -2.7x2 + 2.7x2 Combine like terms: -2.7x2 + 2.7x2 = 0.0 -5 + -32x + 2.7x2 = 0.0 Begin completing the square. Divide all terms by 2.7 the coefficient of the squared term: Divide each side by '2.7'. -1.851851852 + -11.85185185x + x2 = 0 Move the constant term to the right: Add '1.851851852' to each side of the equation. -1.851851852 + -11.85185185x + 1.851851852 + x2 = 0 + 1.851851852 Reorder the terms: -1.851851852 + 1.851851852 + -11.85185185x + x2 = 0 + 1.851851852 Combine like terms: -1.851851852 + 1.851851852 = 0.000000000 0.000000000 + -11.85185185x + x2 = 0 + 1.851851852 -11.85185185x + x2 = 0 + 1.851851852 Combine like terms: 0 + 1.851851852 = 1.851851852 -11.85185185x + x2 = 1.851851852 The x term is -11.85185185x. Take half its coefficient (-5.925925925). Square it (35.11659807) and add it to both sides. Add '35.11659807' to each side of the equation. -11.85185185x + 35.11659807 + x2 = 1.851851852 + 35.11659807 Reorder the terms: 35.11659807 + -11.85185185x + x2 = 1.851851852 + 35.11659807 Combine like terms: 1.851851852 + 35.11659807 = 36.968449922 35.11659807 + -11.85185185x + x2 = 36.968449922 Factor a perfect square on the left side: (x + -5.925925925)(x + -5.925925925) = 36.968449922 Calculate the square root of the right side: 6.080168577 Break this problem into two subproblems by setting (x + -5.925925925) equal to 6.080168577 and -6.080168577.Subproblem 1
x + -5.925925925 = 6.080168577 Simplifying x + -5.925925925 = 6.080168577 Reorder the terms: -5.925925925 + x = 6.080168577 Solving -5.925925925 + x = 6.080168577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.925925925' to each side of the equation. -5.925925925 + 5.925925925 + x = 6.080168577 + 5.925925925 Combine like terms: -5.925925925 + 5.925925925 = 0.000000000 0.000000000 + x = 6.080168577 + 5.925925925 x = 6.080168577 + 5.925925925 Combine like terms: 6.080168577 + 5.925925925 = 12.006094502 x = 12.006094502 Simplifying x = 12.006094502Subproblem 2
x + -5.925925925 = -6.080168577 Simplifying x + -5.925925925 = -6.080168577 Reorder the terms: -5.925925925 + x = -6.080168577 Solving -5.925925925 + x = -6.080168577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.925925925' to each side of the equation. -5.925925925 + 5.925925925 + x = -6.080168577 + 5.925925925 Combine like terms: -5.925925925 + 5.925925925 = 0.000000000 0.000000000 + x = -6.080168577 + 5.925925925 x = -6.080168577 + 5.925925925 Combine like terms: -6.080168577 + 5.925925925 = -0.154242652 x = -0.154242652 Simplifying x = -0.154242652Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.006094502, -0.154242652}
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