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Simplifying 2.3x2 + 1.2x + -4.9 = 0 Reorder the terms: -4.9 + 1.2x + 2.3x2 = 0 Solving -4.9 + 1.2x + 2.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -2.130434783 + 0.5217391304x + x2 = 0 Move the constant term to the right: Add '2.130434783' to each side of the equation. -2.130434783 + 0.5217391304x + 2.130434783 + x2 = 0 + 2.130434783 Reorder the terms: -2.130434783 + 2.130434783 + 0.5217391304x + x2 = 0 + 2.130434783 Combine like terms: -2.130434783 + 2.130434783 = 0.000000000 0.000000000 + 0.5217391304x + x2 = 0 + 2.130434783 0.5217391304x + x2 = 0 + 2.130434783 Combine like terms: 0 + 2.130434783 = 2.130434783 0.5217391304x + x2 = 2.130434783 The x term is 0.5217391304x. Take half its coefficient (0.2608695652). Square it (0.06805293005) and add it to both sides. Add '0.06805293005' to each side of the equation. 0.5217391304x + 0.06805293005 + x2 = 2.130434783 + 0.06805293005 Reorder the terms: 0.06805293005 + 0.5217391304x + x2 = 2.130434783 + 0.06805293005 Combine like terms: 2.130434783 + 0.06805293005 = 2.19848771305 0.06805293005 + 0.5217391304x + x2 = 2.19848771305 Factor a perfect square on the left side: (x + 0.2608695652)(x + 0.2608695652) = 2.19848771305 Calculate the square root of the right side: 1.482729818 Break this problem into two subproblems by setting (x + 0.2608695652) equal to 1.482729818 and -1.482729818.Subproblem 1
x + 0.2608695652 = 1.482729818 Simplifying x + 0.2608695652 = 1.482729818 Reorder the terms: 0.2608695652 + x = 1.482729818 Solving 0.2608695652 + x = 1.482729818 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2608695652' to each side of the equation. 0.2608695652 + -0.2608695652 + x = 1.482729818 + -0.2608695652 Combine like terms: 0.2608695652 + -0.2608695652 = 0.0000000000 0.0000000000 + x = 1.482729818 + -0.2608695652 x = 1.482729818 + -0.2608695652 Combine like terms: 1.482729818 + -0.2608695652 = 1.2218602528 x = 1.2218602528 Simplifying x = 1.2218602528Subproblem 2
x + 0.2608695652 = -1.482729818 Simplifying x + 0.2608695652 = -1.482729818 Reorder the terms: 0.2608695652 + x = -1.482729818 Solving 0.2608695652 + x = -1.482729818 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2608695652' to each side of the equation. 0.2608695652 + -0.2608695652 + x = -1.482729818 + -0.2608695652 Combine like terms: 0.2608695652 + -0.2608695652 = 0.0000000000 0.0000000000 + x = -1.482729818 + -0.2608695652 x = -1.482729818 + -0.2608695652 Combine like terms: -1.482729818 + -0.2608695652 = -1.7435993832 x = -1.7435993832 Simplifying x = -1.7435993832Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2218602528, -1.7435993832}
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