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Simplifying 2.3x2 + 8x + -2.45 = 0 Reorder the terms: -2.45 + 8x + 2.3x2 = 0 Solving -2.45 + 8x + 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'. -1.065217391 + 3.47826087x + x2 = 0 Move the constant term to the right: Add '1.065217391' to each side of the equation. -1.065217391 + 3.47826087x + 1.065217391 + x2 = 0 + 1.065217391 Reorder the terms: -1.065217391 + 1.065217391 + 3.47826087x + x2 = 0 + 1.065217391 Combine like terms: -1.065217391 + 1.065217391 = 0.000000000 0.000000000 + 3.47826087x + x2 = 0 + 1.065217391 3.47826087x + x2 = 0 + 1.065217391 Combine like terms: 0 + 1.065217391 = 1.065217391 3.47826087x + x2 = 1.065217391 The x term is 3.47826087x. Take half its coefficient (1.739130435). Square it (3.024574670) and add it to both sides. Add '3.024574670' to each side of the equation. 3.47826087x + 3.024574670 + x2 = 1.065217391 + 3.024574670 Reorder the terms: 3.024574670 + 3.47826087x + x2 = 1.065217391 + 3.024574670 Combine like terms: 1.065217391 + 3.024574670 = 4.089792061 3.024574670 + 3.47826087x + x2 = 4.089792061 Factor a perfect square on the left side: (x + 1.739130435)(x + 1.739130435) = 4.089792061 Calculate the square root of the right side: 2.022323431 Break this problem into two subproblems by setting (x + 1.739130435) equal to 2.022323431 and -2.022323431.Subproblem 1
x + 1.739130435 = 2.022323431 Simplifying x + 1.739130435 = 2.022323431 Reorder the terms: 1.739130435 + x = 2.022323431 Solving 1.739130435 + x = 2.022323431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.739130435' to each side of the equation. 1.739130435 + -1.739130435 + x = 2.022323431 + -1.739130435 Combine like terms: 1.739130435 + -1.739130435 = 0.000000000 0.000000000 + x = 2.022323431 + -1.739130435 x = 2.022323431 + -1.739130435 Combine like terms: 2.022323431 + -1.739130435 = 0.283192996 x = 0.283192996 Simplifying x = 0.283192996Subproblem 2
x + 1.739130435 = -2.022323431 Simplifying x + 1.739130435 = -2.022323431 Reorder the terms: 1.739130435 + x = -2.022323431 Solving 1.739130435 + x = -2.022323431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.739130435' to each side of the equation. 1.739130435 + -1.739130435 + x = -2.022323431 + -1.739130435 Combine like terms: 1.739130435 + -1.739130435 = 0.000000000 0.000000000 + x = -2.022323431 + -1.739130435 x = -2.022323431 + -1.739130435 Combine like terms: -2.022323431 + -1.739130435 = -3.761453866 x = -3.761453866 Simplifying x = -3.761453866Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.283192996, -3.761453866}
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