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Simplifying 5x2 + 7x + 3 = 16 Reorder the terms: 3 + 7x + 5x2 = 16 Solving 3 + 7x + 5x2 = 16 Solving for variable 'x'. Reorder the terms: 3 + -16 + 7x + 5x2 = 16 + -16 Combine like terms: 3 + -16 = -13 -13 + 7x + 5x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -13 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 1.4x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 1.4x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 1.4x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 1.4x + x2 = 0 + 2.6 1.4x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 1.4x + x2 = 2.6 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 2.6 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 2.6 + 0.49 Combine like terms: 2.6 + 0.49 = 3.09 0.49 + 1.4x + x2 = 3.09 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 3.09 Calculate the square root of the right side: 1.757839583 Break this problem into two subproblems by setting (x + 0.7) equal to 1.757839583 and -1.757839583.Subproblem 1
x + 0.7 = 1.757839583 Simplifying x + 0.7 = 1.757839583 Reorder the terms: 0.7 + x = 1.757839583 Solving 0.7 + x = 1.757839583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 1.757839583 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 1.757839583 + -0.7 x = 1.757839583 + -0.7 Combine like terms: 1.757839583 + -0.7 = 1.057839583 x = 1.057839583 Simplifying x = 1.057839583Subproblem 2
x + 0.7 = -1.757839583 Simplifying x + 0.7 = -1.757839583 Reorder the terms: 0.7 + x = -1.757839583 Solving 0.7 + x = -1.757839583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -1.757839583 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -1.757839583 + -0.7 x = -1.757839583 + -0.7 Combine like terms: -1.757839583 + -0.7 = -2.457839583 x = -2.457839583 Simplifying x = -2.457839583Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.057839583, -2.457839583}
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