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Simplifying 4x2 + 5x + -21 = -3 Reorder the terms: -21 + 5x + 4x2 = -3 Solving -21 + 5x + 4x2 = -3 Solving for variable 'x'. Reorder the terms: -21 + 3 + 5x + 4x2 = -3 + 3 Combine like terms: -21 + 3 = -18 -18 + 5x + 4x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -18 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 1.25x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 1.25x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 1.25x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 1.25x + x2 = 0 + 4.5 1.25x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 1.25x + x2 = 4.5 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 4.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 4.5 + 0.390625 Combine like terms: 4.5 + 0.390625 = 4.890625 0.390625 + 1.25x + x2 = 4.890625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (x + 0.625) equal to 2.211475752 and -2.211475752.Subproblem 1
x + 0.625 = 2.211475752 Simplifying x + 0.625 = 2.211475752 Reorder the terms: 0.625 + x = 2.211475752 Solving 0.625 + x = 2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 2.211475752 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 2.211475752 + -0.625 x = 2.211475752 + -0.625 Combine like terms: 2.211475752 + -0.625 = 1.586475752 x = 1.586475752 Simplifying x = 1.586475752Subproblem 2
x + 0.625 = -2.211475752 Simplifying x + 0.625 = -2.211475752 Reorder the terms: 0.625 + x = -2.211475752 Solving 0.625 + x = -2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -2.211475752 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -2.211475752 + -0.625 x = -2.211475752 + -0.625 Combine like terms: -2.211475752 + -0.625 = -2.836475752 x = -2.836475752 Simplifying x = -2.836475752Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.586475752, -2.836475752}
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