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Simplifying 25x2 + 28x + -72 = 0 Reorder the terms: -72 + 28x + 25x2 = 0 Solving -72 + 28x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.88 + 1.12x + x2 = 0 Move the constant term to the right: Add '2.88' to each side of the equation. -2.88 + 1.12x + 2.88 + x2 = 0 + 2.88 Reorder the terms: -2.88 + 2.88 + 1.12x + x2 = 0 + 2.88 Combine like terms: -2.88 + 2.88 = 0.00 0.00 + 1.12x + x2 = 0 + 2.88 1.12x + x2 = 0 + 2.88 Combine like terms: 0 + 2.88 = 2.88 1.12x + x2 = 2.88 The x term is 1.12x. Take half its coefficient (0.56). Square it (0.3136) and add it to both sides. Add '0.3136' to each side of the equation. 1.12x + 0.3136 + x2 = 2.88 + 0.3136 Reorder the terms: 0.3136 + 1.12x + x2 = 2.88 + 0.3136 Combine like terms: 2.88 + 0.3136 = 3.1936 0.3136 + 1.12x + x2 = 3.1936 Factor a perfect square on the left side: (x + 0.56)(x + 0.56) = 3.1936 Calculate the square root of the right side: 1.787064632 Break this problem into two subproblems by setting (x + 0.56) equal to 1.787064632 and -1.787064632.Subproblem 1
x + 0.56 = 1.787064632 Simplifying x + 0.56 = 1.787064632 Reorder the terms: 0.56 + x = 1.787064632 Solving 0.56 + x = 1.787064632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.56' to each side of the equation. 0.56 + -0.56 + x = 1.787064632 + -0.56 Combine like terms: 0.56 + -0.56 = 0.00 0.00 + x = 1.787064632 + -0.56 x = 1.787064632 + -0.56 Combine like terms: 1.787064632 + -0.56 = 1.227064632 x = 1.227064632 Simplifying x = 1.227064632Subproblem 2
x + 0.56 = -1.787064632 Simplifying x + 0.56 = -1.787064632 Reorder the terms: 0.56 + x = -1.787064632 Solving 0.56 + x = -1.787064632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.56' to each side of the equation. 0.56 + -0.56 + x = -1.787064632 + -0.56 Combine like terms: 0.56 + -0.56 = 0.00 0.00 + x = -1.787064632 + -0.56 x = -1.787064632 + -0.56 Combine like terms: -1.787064632 + -0.56 = -2.347064632 x = -2.347064632 Simplifying x = -2.347064632Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.227064632, -2.347064632}
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