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Simplifying 5x2 + 3x + 24 = 47 Reorder the terms: 24 + 3x + 5x2 = 47 Solving 24 + 3x + 5x2 = 47 Solving for variable 'x'. Reorder the terms: 24 + -47 + 3x + 5x2 = 47 + -47 Combine like terms: 24 + -47 = -23 -23 + 3x + 5x2 = 47 + -47 Combine like terms: 47 + -47 = 0 -23 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.6 + 0.6x + x2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + 0.6x + 4.6 + x2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + 0.6x + x2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + 0.6x + x2 = 0 + 4.6 0.6x + x2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 0.6x + x2 = 4.6 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 4.6 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 4.6 + 0.09 Combine like terms: 4.6 + 0.09 = 4.69 0.09 + 0.6x + x2 = 4.69 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 4.69 Calculate the square root of the right side: 2.165640783 Break this problem into two subproblems by setting (x + 0.3) equal to 2.165640783 and -2.165640783.Subproblem 1
x + 0.3 = 2.165640783 Simplifying x + 0.3 = 2.165640783 Reorder the terms: 0.3 + x = 2.165640783 Solving 0.3 + x = 2.165640783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 2.165640783 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.165640783 + -0.3 x = 2.165640783 + -0.3 Combine like terms: 2.165640783 + -0.3 = 1.865640783 x = 1.865640783 Simplifying x = 1.865640783Subproblem 2
x + 0.3 = -2.165640783 Simplifying x + 0.3 = -2.165640783 Reorder the terms: 0.3 + x = -2.165640783 Solving 0.3 + x = -2.165640783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -2.165640783 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.165640783 + -0.3 x = -2.165640783 + -0.3 Combine like terms: -2.165640783 + -0.3 = -2.465640783 x = -2.465640783 Simplifying x = -2.465640783Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.865640783, -2.465640783}
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