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Simplifying 3.8x2 + 4x + -4.9 = 0 Reorder the terms: -4.9 + 4x + 3.8x2 = 0 Solving -4.9 + 4x + 3.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.8 the coefficient of the squared term: Divide each side by '3.8'. -1.289473684 + 1.052631579x + x2 = 0 Move the constant term to the right: Add '1.289473684' to each side of the equation. -1.289473684 + 1.052631579x + 1.289473684 + x2 = 0 + 1.289473684 Reorder the terms: -1.289473684 + 1.289473684 + 1.052631579x + x2 = 0 + 1.289473684 Combine like terms: -1.289473684 + 1.289473684 = 0.000000000 0.000000000 + 1.052631579x + x2 = 0 + 1.289473684 1.052631579x + x2 = 0 + 1.289473684 Combine like terms: 0 + 1.289473684 = 1.289473684 1.052631579x + x2 = 1.289473684 The x term is 1.052631579x. Take half its coefficient (0.5263157895). Square it (0.2770083103) and add it to both sides. Add '0.2770083103' to each side of the equation. 1.052631579x + 0.2770083103 + x2 = 1.289473684 + 0.2770083103 Reorder the terms: 0.2770083103 + 1.052631579x + x2 = 1.289473684 + 0.2770083103 Combine like terms: 1.289473684 + 0.2770083103 = 1.5664819943 0.2770083103 + 1.052631579x + x2 = 1.5664819943 Factor a perfect square on the left side: (x + 0.5263157895)(x + 0.5263157895) = 1.5664819943 Calculate the square root of the right side: 1.251591784 Break this problem into two subproblems by setting (x + 0.5263157895) equal to 1.251591784 and -1.251591784.Subproblem 1
x + 0.5263157895 = 1.251591784 Simplifying x + 0.5263157895 = 1.251591784 Reorder the terms: 0.5263157895 + x = 1.251591784 Solving 0.5263157895 + x = 1.251591784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5263157895' to each side of the equation. 0.5263157895 + -0.5263157895 + x = 1.251591784 + -0.5263157895 Combine like terms: 0.5263157895 + -0.5263157895 = 0.0000000000 0.0000000000 + x = 1.251591784 + -0.5263157895 x = 1.251591784 + -0.5263157895 Combine like terms: 1.251591784 + -0.5263157895 = 0.7252759945 x = 0.7252759945 Simplifying x = 0.7252759945Subproblem 2
x + 0.5263157895 = -1.251591784 Simplifying x + 0.5263157895 = -1.251591784 Reorder the terms: 0.5263157895 + x = -1.251591784 Solving 0.5263157895 + x = -1.251591784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5263157895' to each side of the equation. 0.5263157895 + -0.5263157895 + x = -1.251591784 + -0.5263157895 Combine like terms: 0.5263157895 + -0.5263157895 = 0.0000000000 0.0000000000 + x = -1.251591784 + -0.5263157895 x = -1.251591784 + -0.5263157895 Combine like terms: -1.251591784 + -0.5263157895 = -1.7779075735 x = -1.7779075735 Simplifying x = -1.7779075735Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7252759945, -1.7779075735}
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