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Simplifying 5x2 + 6 + 2x = 21 Reorder the terms: 6 + 2x + 5x2 = 21 Solving 6 + 2x + 5x2 = 21 Solving for variable 'x'. Reorder the terms: 6 + -21 + 2x + 5x2 = 21 + -21 Combine like terms: 6 + -21 = -15 -15 + 2x + 5x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -15 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + 0.4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.4x + x2 = 0 + 3 0.4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.4x + x2 = 3 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 3 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 3 + 0.04 Combine like terms: 3 + 0.04 = 3.04 0.04 + 0.4x + x2 = 3.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (x + 0.2) equal to 1.743559577 and -1.743559577.Subproblem 1
x + 0.2 = 1.743559577 Simplifying x + 0.2 = 1.743559577 Reorder the terms: 0.2 + x = 1.743559577 Solving 0.2 + x = 1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.743559577 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.743559577 + -0.2 x = 1.743559577 + -0.2 Combine like terms: 1.743559577 + -0.2 = 1.543559577 x = 1.543559577 Simplifying x = 1.543559577Subproblem 2
x + 0.2 = -1.743559577 Simplifying x + 0.2 = -1.743559577 Reorder the terms: 0.2 + x = -1.743559577 Solving 0.2 + x = -1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.743559577 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.743559577 + -0.2 x = -1.743559577 + -0.2 Combine like terms: -1.743559577 + -0.2 = -1.943559577 x = -1.943559577 Simplifying x = -1.943559577Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.543559577, -1.943559577}
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