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Simplifying 5x2 + 16x + 11.25 = 0 Reorder the terms: 11.25 + 16x + 5x2 = 0 Solving 11.25 + 16x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.25 + 3.2x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 3.2x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 3.2x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 3.2x + x2 = 0 + -2.25 3.2x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 3.2x + x2 = -2.25 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -2.25 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -2.25 + 2.56 Combine like terms: -2.25 + 2.56 = 0.31 2.56 + 3.2x + x2 = 0.31 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 0.31 Calculate the square root of the right side: 0.556776436 Break this problem into two subproblems by setting (x + 1.6) equal to 0.556776436 and -0.556776436.Subproblem 1
x + 1.6 = 0.556776436 Simplifying x + 1.6 = 0.556776436 Reorder the terms: 1.6 + x = 0.556776436 Solving 1.6 + x = 0.556776436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 0.556776436 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 0.556776436 + -1.6 x = 0.556776436 + -1.6 Combine like terms: 0.556776436 + -1.6 = -1.043223564 x = -1.043223564 Simplifying x = -1.043223564Subproblem 2
x + 1.6 = -0.556776436 Simplifying x + 1.6 = -0.556776436 Reorder the terms: 1.6 + x = -0.556776436 Solving 1.6 + x = -0.556776436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -0.556776436 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -0.556776436 + -1.6 x = -0.556776436 + -1.6 Combine like terms: -0.556776436 + -1.6 = -2.156776436 x = -2.156776436 Simplifying x = -2.156776436Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.043223564, -2.156776436}
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