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Simplifying 4x2 + -5x + 3 = 15 Reorder the terms: 3 + -5x + 4x2 = 15 Solving 3 + -5x + 4x2 = 15 Solving for variable 'x'. Reorder the terms: 3 + -15 + -5x + 4x2 = 15 + -15 Combine like terms: 3 + -15 = -12 -12 + -5x + 4x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -12 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + -1.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.25x + x2 = 0 + 3 -1.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.25x + x2 = 3 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 = 3 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 3 + 0.390625 Combine like terms: 3 + 0.390625 = 3.390625 0.390625 + -1.25x + x2 = 3.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (x + -0.625) equal to 1.841364983 and -1.841364983.Subproblem 1
x + -0.625 = 1.841364983 Simplifying x + -0.625 = 1.841364983 Reorder the terms: -0.625 + x = 1.841364983 Solving -0.625 + x = 1.841364983 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 = 1.841364983 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.841364983 + 0.625 x = 1.841364983 + 0.625 Combine like terms: 1.841364983 + 0.625 = 2.466364983 x = 2.466364983 Simplifying x = 2.466364983Subproblem 2
x + -0.625 = -1.841364983 Simplifying x + -0.625 = -1.841364983 Reorder the terms: -0.625 + x = -1.841364983 Solving -0.625 + x = -1.841364983 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 = -1.841364983 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.841364983 + 0.625 x = -1.841364983 + 0.625 Combine like terms: -1.841364983 + 0.625 = -1.216364983 x = -1.216364983 Simplifying x = -1.216364983Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.466364983, -1.216364983}
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