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Simplifying 10x2 + 48x + 28 = 0 Reorder the terms: 28 + 48x + 10x2 = 0 Solving 28 + 48x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 24x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + 24x + 5x2)' equal to zero and attempt to solve: Simplifying 14 + 24x + 5x2 = 0 Solving 14 + 24x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 4.8x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 4.8x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 4.8x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 4.8x + x2 = 0 + -2.8 4.8x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 4.8x + x2 = -2.8 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = -2.8 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = -2.8 + 5.76 Combine like terms: -2.8 + 5.76 = 2.96 5.76 + 4.8x + x2 = 2.96 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 2.96 Calculate the square root of the right side: 1.720465053 Break this problem into two subproblems by setting (x + 2.4) equal to 1.720465053 and -1.720465053.Subproblem 1
x + 2.4 = 1.720465053 Simplifying x + 2.4 = 1.720465053 Reorder the terms: 2.4 + x = 1.720465053 Solving 2.4 + x = 1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 1.720465053 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 1.720465053 + -2.4 x = 1.720465053 + -2.4 Combine like terms: 1.720465053 + -2.4 = -0.679534947 x = -0.679534947 Simplifying x = -0.679534947Subproblem 2
x + 2.4 = -1.720465053 Simplifying x + 2.4 = -1.720465053 Reorder the terms: 2.4 + x = -1.720465053 Solving 2.4 + x = -1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -1.720465053 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -1.720465053 + -2.4 x = -1.720465053 + -2.4 Combine like terms: -1.720465053 + -2.4 = -4.120465053 x = -4.120465053 Simplifying x = -4.120465053Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.679534947, -4.120465053}Solution
x = {-0.679534947, -4.120465053}
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